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STATISTICS IN BUSINESS 
 
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STATISTICS 
 
 IN 
 
 BUSINESS 
 
 THEIR ANALYSIS, CHARTING AND USE 
 
 BY 
 HORACE SECRIST, Ph. D. 
 
 PROFESBOB OP ECONOMICS AND STATISTICS, NORTHWESTERN 
 UNIVERSITY, AND DIRECTOR OF THE BUREAU OF BUSINESS 
 RESEARCH, NORTHWESTERN UNIVERSITT SCHOOL OF COMMERCE 
 FORMERLY, STATISTICIAN, TONNAGE SECTION, DIVISION OF 
 PLANNING AND STATISTICS, UNITED STATES SHIPPING BOARD 
 author: an INTRODUCTION TO STATISTICAL METHODS 
 
 First Edition 
 Third Impres>5Ion 
 
 McGRAW-HILL BOOK COMPANY, Inc. 
 
 NEW YORK: 370 SEVENTH AVENUE 
 
 LONDON: 6 & 8 BOUVERIE ST., E. C. 4 
 
 1921 
 
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 coptkight, 1920, by the 
 McGkaw-Hill Book Company, Inc. 
 
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PREFACE 
 
 This volume has been prepared primarily for 
 business executives, although it is hoped that it will 
 be of use in Schools of Commerce. It aims to present 
 briefly and concretely the reasons why statistics 
 should be used in business analysis, and to illustrate 
 how and with what effect they may be applied in the 
 solution of business problems. 
 
 The volume is not intended to be a treatise on 
 statistics. Its purpose is to serve as a handbook for 
 executives and others in responsible positions in the 
 application of business statistics to problems which 
 currently arise. To this end, the discussion is of a 
 practical character — especial attention being given 
 to the use of graphs and charts. Both good and 
 bad statistical usages are developed by means of 
 illustrations, and rules are formulated which will serve 
 to guide executives at each step in business analysis 
 by means of statistics. 
 
 The treatment is intentionally brief. What is most 
 needed, in the writer's judgment, is a terse, concrete 
 discussion of statistics in business which executives will 
 read, and which will serve to suggest the place which 
 statistics should have as a controlling factor in business 
 planning. This need, this book endeavors to meet. 
 
 The writer is indebted to his colleagues, Professors 
 Walter K. Smart and Franklin Bliss Snyder, for 
 carefully reading the manuscript, and to Professor 
 Homer B. Vanderblue and Mr. A. W. T. Ogilvie 
 for helpful suggestions concerning the applications of 
 statistics in business. 
 
 Horace Secrist. 
 
 Northwestern Universitt, 
 December 15, 1919. 
 
 vii 
 
CONTENTS 
 
 Chaptsb Paqe 
 
 I. Modern Business and Fact Analysis 1 
 
 II. The Facts of Business 5 
 
 III. Recognizing and Securing the Facts 26 
 
 IV. Classifying and Tabulating the Facts 41 
 
 V. Presenting the Facts — Graphics 55 
 
 VI. Summarizing the Facts — Averages and Other 
 
 Means 97 
 
 VII. Comparison and the Establishment of Business 
 
 Principles and Standards 124 
 
 Index 131 
 
 IX 
 
STATISTICS IN BUSINESS 
 
 THEIR ANALYSIS. CHARTING AND USE 
 
 CHAPTER I 
 
 MODERN BUSINESS AND FACT ANALYSIS 
 
 Business, as known to the producer, to the con- 
 sumer, and to the pubUc generally, is personified in 
 the merchant, the banker, the manufacturer, the 
 farmer. Representatives of each class may be known 
 personally, but as a whole, business is seen as the 
 impersonal organizations and relations upon which 
 production, distribution, and exchange depend. 
 
 Some businesses are small, some are large. Some 
 are the result of almost world-wide activity and fore- 
 sight, while some are of local significance and of limited 
 outlook. Whatever their size, or the extent of their 
 activities or influence, they are the operating units 
 through which the wants of mankind are satisfied. 
 They are individual, partnership, and corporate enter- 
 prises. To some, they represent accumulated wealth 
 operating only as profit makers; to others, they are 
 primarily service units, providing the necessities, the 
 comforts, and luxuries of life. They are coopera- 
 tive organizations, through which modern complex 
 society, by the use of natural resources, labor, and 
 inventive genius, not only satisfies its wants, but also 
 expresses its creative faculties. To the business man, 
 
 1 
 
2 STATISTICS IN BUSINESS 
 
 as such, they are the organized machinery for making 
 profits; to the public, as consumer, they are the means 
 of satisfying wants. 
 
 Viewed from either angle, such business units rest 
 on cooperation, trust, confidence, and good-will. 
 Society as a whole, and as classified groups, realizes 
 its economic life through them. This has always 
 been so, but the type of the modern business is differ- 
 ent from the ancient. Modern industrial life is com- 
 plex, the units are relatively large, the classes dealing 
 with them diverse, and the relations between them 
 impersonal. Some of them must meet world com- 
 petition; others, only that which is local. But they 
 must all deal with an increasingly discriminating 
 public, and with an intensified competition. Compe- 
 tition applies to price, service, and cost. Costs extend 
 to a whole world of commodities, and service is drawn 
 from ever extending areas, and from an increasingly 
 independent labor market. Prices are governed by 
 local and by national conditions, and the standards 
 of service are progressively severe and exacting. 
 Modern business cannot ignore these facts, nor blindly 
 meet the issues which they raise. The day of chance 
 gains and treasure trove is passing, if it is not past. 
 The possession and use of facts in business today spell 
 the difference between success and failure. No longer 
 is it enough to trust to luck and to rule-of-thumb 
 methods. Economic and business judgments must 
 be based on facts, properly analyzed and interpreted. 
 Appeal to force of custom and long continued practice 
 no longer suffices as a basis for an economic program, 
 or business judgment. . Ours is the age of the concrete. 
 The reasons for success or failure must be sought in 
 
MODERN BUSINESS AND FACT ANALYSIS 3 
 
 realities. A fool's paradise in business brings with it 
 its' just reward. 
 
 So strongly has the need for classified knowledge 
 come to be felt by successful business during the last 
 two decades that a true accounting is today considered 
 not only desirable, but indispensable in industry. 
 There are some who still say, "We keep no accounts, 
 we are successful business men, " but this tribe is fast 
 becoming extinct. Accounting has clarified the oc- 
 casion for profit and for loss, and accurately stated 
 the amount. Business has aimed to be intelligent as 
 to past operation; it has only here and there begun to 
 be scientific as to policy and future activity. A strict 
 accounting serves to meet the problems internally; 
 statistics or fact analysis will meet them generally. 
 
 Now, fact analysis is nothing but an application of 
 scientific method. What does it imply? Scientific 
 method in industry means recognizing facts and acting 
 in the light of their interpretation. It means taking 
 note of small differences, seeking for the similarities 
 and basic truths which govern business and industrial 
 relations, and being guided by them. It means fore- 
 sight, rather than hindsight; planning rather than 
 customary behavior. It means innovation and change, 
 if an impersonal analysis of the facts suggests them. 
 It means fearlessness and respect for facts. 
 
 Scientific analysis of business and industrial prob- 
 lems requires, first, a point of view, and second, a 
 method. The point of view is an unconditional 
 demand for the truth; the method is (1) intelligent 
 observation; (2) impartial analysis; (3) logical infer- 
 ence; and (4) sincere application of the conclusion 
 reached to the problem to which the facts and obser- 
 
4 STATISTICS IN BUSINESS 
 
 vation apply. Business facts are numerous and in- 
 creasingly complex; they are ever changing in content 
 and application. To know them requires keen obser- 
 vation; to secure them, organization; and to apply 
 them, determination and business integrity. There 
 is a science of business and industry, the underlying 
 facts and principles of which can be determined, and 
 they must be applied, if planning and foresight are 
 to take the place of guessing and rule-of-thumb action. 
 Business and industry need facts, but most of all 
 they need analysis of facts and application of them to 
 current problems. Business will not run on, but 
 down, on the momentum of customary action. Fresh 
 and continuous analysis of facts is indispensable. 
 The need is for an appreciation of facts, an ability 
 to observe truthfully the conditions which produce 
 them, and a determination logically to use them in such 
 a way that they will serve as rules for business guidance. 
 
CHAPTER II 
 THE FACTS OF BUSINESS 
 
 What the facts of business are which need to be 
 recognized, understood, and applied to business prob- 
 lems, it is the purpose of this chapter to answer. But 
 first, the nature of a " fact " must be considered. The 
 facts which can be used scientifically in business and 
 industry, must be commensurable. They must be 
 stated, enumerated, or estimated according to suitable 
 standards of accuracy; they must be collected system- 
 atically for a definite purpose, and must be capable 
 of being used comparatively. They are the raw 
 material upon which positive conclusions are to be 
 based, and, therefore, must be definite, measurable 
 quantities. 
 
 When they exist ready for use, they must be scruti- 
 nized and their meaning understood. When they do 
 not exist ready at hand, they must be collected or 
 secured with these thoughts in mind. How they may 
 be secured and the tests to which they must be sub- 
 jected, it is the purpose of the following chapter to 
 explain. It is the purpose of this chapter to describe 
 briefly the kinds of facts by which business and 
 industry must be positively guided. 
 
 Business and industry may be classified according 
 to the functions which are performed. From this 
 angle, the producing, selling, marketing, transporting, 
 
 5 
 
6 STATISTICS IN BUSINESS 
 
 and credit-making services are significant. For in- 
 stance, industry is designed for production purposes. 
 Raw materials, finished and partly finished commodi- 
 ties, find their way into the great maw of organized 
 industry, to be turned out as finished products, ready 
 for consumption, or as partly finished products, to 
 be turned back again into industry, and subjected to 
 further alterations, combinations, or changes. Trans- 
 portation, selling, marketing, and credit extending are 
 all incidental to production and preliminary to final 
 consumption. 
 
 What detailed facts must be known about these 
 processes, if they are to be intelligently conducted? 
 Socialists and others characterize competitive indus- 
 try as wasteful, meaningless, and anarchistic in many 
 of its processes, and the criticism to a large degree is 
 valid. In a given plant, purpose and order may 
 obtain, but within industry as a whole, chaos may 
 reign. How can private industry meet the challenge 
 of its opponents, and justify itself through the appli- 
 cation of scientific methods? 
 
 Production implies the creation of commodities and 
 services in response to, or in anticipation of, demand. 
 It requires continuous and uninterrupted additions 
 of capital, wide and certain markets, an uninterrupted 
 flow of raw materials, and a contented and industrious, 
 labor force. In order for production to be conducted 
 intelligently, the contingencies affecting any and all 
 of these factors must be definitely known and dis- 
 counted. If iron or steel constitutes the basic raw 
 material upon which an industry depends, the peculi- 
 arities of its production, the sources from which it is 
 drawn, its price determining factors, transportation 
 
THE FACTS OF BUSINESS 7 
 
 difficulties and facilities, and its relationship to credit 
 conditions must be appreciated. These can hardly 
 be known in detail by a single producer for a single 
 supplier, but as reflected in that indefinite, yet very 
 real, thing known as the market, they are determin- 
 able. There are capital, labor, and credit markets, 
 and these the business man should know and be able 
 to interpret. Moreover, the conditions governing 
 transportation and consumption are patent to those 
 who have eyes to see and understanding to appreciate. 
 The producer, like others in the intricate organization 
 of business and industry, must realize the fact that 
 economic life expresses itself in the basic facts of crop 
 production, credit extensions, business failure, capital 
 formation, labor satisfaction and distrust. The view 
 of the forest, however, must not be confounded with 
 that of the trees. The view points must be com- 
 plementary. This is no less true for other types of 
 business than it is for the producer. 
 
 A more intimate view of some business functions in 
 relation to fact analysis will be of interest. Why are 
 goods, either as raw material or as finished products, 
 imported? How does the imported compare with 
 the domestic product in relation to price, certainty 
 of supply, costs in transportation, ease in handling? 
 How does it stand in relation to substitutes and com- 
 petitive conditions? Why push export sales? Are 
 home markets exhausted, or has the point of diminish- 
 ing returns been reached? Is the foreign consumer 
 known as well as the domestic; are there race 
 prejudices, national peculiarities and trade customs, 
 which must be overcome ? Have these been measured , 
 and their significance considered in the action taken ? 
 
8 STATISTICS IN BUSINESS 
 
 Have the facts been determined in shaping the poUcy, 
 or is the line of action the customary or convenient 
 one? "Look and see," is the perpetual injunction 
 with which industry must ever comply. 
 
 But "seeing" is discriminating. To those who are 
 business blind, markets, price policies and labor 
 appear as homogeneous phenomena to be treated by 
 fixed formulae. The solution of problems is thought 
 to be automatic. To those who really look and ' ' see," 
 all business problems break up into numerous phases, 
 each requiring different treatment as principles of psy- 
 chology, social and labor theories, etc., are involved. 
 
 But business and industry may also be looked at 
 from another angle. In both, the facts of labor, for 
 instance, must be known. What wages are paid, 
 and why ? What are the living conditions in industry ? 
 Do they tend to foster a spirit of confidence and good- 
 will, or to play upon and accentuate industrial ill-will ? 
 What are the sources and race characteristics of the 
 labor force, and how are these related to questions of 
 strikes, unrest, sabotage, unemployment, accidents, 
 labor turn-over? Is only labor power secured when a 
 changed policy would guarantee labor interest? Is 
 industrial good-will or ill-will, capitalized? 
 
 Other facts, bearing as intimately as those connected 
 with labor on the success of industry, must be sur- 
 veyed and used. Capitalistic or machine methods 
 made modern large-scale industry possible, and busi- 
 ness is becoming increasingly capitalistic; yet the 
 possibilities of machine production, involving round- 
 about, time-consuming, but prolific processes, are 
 only faintly realized. How often today is the intro- 
 duction into industry of capitalistic devices accompa- 
 
THE FACTS OF BUSINESS 9 
 
 nied by an application of scientific method, in order to 
 test their fitness, usefulness, and cost? The hit-and- 
 miss, rule-of-thumb method triumphs in all but the 
 largest and most enterprising industries. The small, 
 struggling, wasteful, and planless business still endures. 
 A long-time point of view, accompanied by observa- 
 tion and experimentation on the economies of par- 
 ticular capital devices, is not the rule. It should be, 
 however, and undoubtedly will be as soon as the 
 business man becomes keenly alive to the logic of 
 facts and the significance of planning in industry. 
 
 Moreover, capital is the result of saving, and takes 
 the form of capital goods, only through investment. 
 Does the modern business man know the investment 
 market? The public is not a homogeneous mass 
 which absorbs so many loans or exudes a certain 
 capital fund. It is composed of discriminating and 
 differentiating groups reacting differently to different 
 conditions of credit, time, risk, and economic return. 
 Moreover, the public does not respond uniformly 
 toward all types of enterprise. To the conservative 
 investor, mining stock is taboo; to the plunger, his 
 forte. Public utility securities, under a given philoso- 
 phy of regulation and the laws of certain states, may 
 be considered as choice investments. Under different 
 philosophy and laws they maybe a drug on the market. 
 Does the business man know the principles of invest- 
 ment, the technique of security issue, and the facts 
 which give investment principles validity? 
 
 Again, is business cognizant of the facts, practices 
 and policies which stimulate confidence and trust, and 
 develop credit ? Business today is almost synonymous 
 with credit, reaching out into the fields where it flows 
 
10 STATISTICS IN BUSINESS 
 
 and retreating where it refuses to go. What creates 
 it, what measures it, what retains it? Only business 
 self-analysis will suggest the answers. Failure to 
 receive credit brings ruin. Of this any business is 
 certain, yet knowing this, the conditions which support 
 credit are ignored because of a frenzied rush for- 
 immediate profits and a disregard of underlying prin- 
 ciples and their analysis. 
 
 The commanding single element in business is, of 
 course, profit. Profit is the difference between costs 
 assumed and prices realized. What are the deter- 
 mining factors in both? Every business man is 
 perpetually straining with them, but how many study 
 scientifically the underlying principles of price deter- 
 mination ? Why are market prices fixed at the current 
 levels? What relations exist between costs of produc- 
 tion and prices, between retail and wholesale prices, 
 between the prices of producers' and consumers' goods, 
 between the prices of complementary goods, between 
 the prices of goods produced under conditions of 
 joint cost? What is the elasticity of a given market? 
 What pressure will it stand? Is it equally elastic at 
 all points, and for all goods? How high can a price be 
 before it reduces sales ; how low must it be to stimulate 
 them? What latent buying power is there and where 
 does it exist? 
 
 5,ule-of-thumb methods and customary behavior 
 will not answer these questions, but the application of 
 scientific method will. Fact analysis in business and 
 industry makes planning intelligent. It gives a sub- 
 stantial basis for constructive judgments. Business 
 under such circumstances is not enshrouded by a halo 
 of obscurities, nor fettered by a web of indefensible 
 
THE FACTS OP BUSINESS 11 
 
 practices. It is still conducted for profit; it still 
 renders service, and appeals for industrial and popular 
 good-will, but it has incorporated in itself the spirit 
 of scientific method. 
 
 It is unnecessary to show how the need for fact 
 analysis extends to other aspects of business. To 
 the reader who has caught the meaning and spirit of 
 scientific method, simply to enumerate a few of 
 these will suffice to call his attention to its further 
 application. Costs, prices, public restrictions, and 
 scientific uses, all apply to land, both as a factor in 
 production and as a marketable commodity. Values 
 for taxes may differ from values for industrial uses. 
 The principles governing rents and tax capitalization 
 offer a broad field for business research. Are taxes 
 shifted, and if so, what are the results due to cost, 
 public discontent, and the distribution of economic 
 burden? What are the relative advantages of land 
 and capital goods under different conditions of busi- 
 ness growth and decline; different conditions of costs 
 of production and tax policies? 
 
 The results of business activities are revealed in the 
 amount of profit; in industrial growth and decline; 
 in the facilities for exchange; and in transportation and 
 industrial and social well-being and discontent. 
 Profits must be studied and the reality of them de- 
 termined. Real, must not be confused with paper, 
 profits. Profits must be thought of both from the 
 short- and the long-time points of view. Failure ade- 
 quately to provide for depreciation and obsolescence 
 may give immediate gains but ultimate loss. What 
 is a reasonable and conservative depreciation rate? 
 Analysis of operation will determine. The rate, we 
 
12 STATISTICS IN BUSINESS 
 
 may be sure, will be different for different properties 
 and for different conditions of operati'on, but the 
 amount cannot be divined in some occult manner, nor 
 left as a "detail" to take care of itself. 
 
 The amount of profit and the business outlook may 
 suggest retrenchment or development. Where shall 
 it be made? Costs are not generally uniform, nor are 
 profits the same on all goods produced or sold. The 
 results of contraction or expansion may be satis- 
 factory as to costs, but ruinous as to profits. The 
 market may be spoiled by additional goods, and costs 
 persist in spite of curtailed production. 
 
 Business, although competitive, is also cooperative. 
 One producer satisfies the demand of another. Trade 
 is more than economic rivalry. The gain to one is not 
 a loss to the other. To satisfy economic wants is the 
 goal of all industrial enterprise, and economy and the 
 scientific point of view suggest that a spirit of hve and 
 let live should characterize industry. The truth must 
 be known, whether it appUes to questions of industrial 
 technique, to matters of industrial relations, or to any 
 other economic fact. The more broadly knowledge is 
 disseminated, and the more general the scientific 
 frame of mind becomes, the more nearly will economic 
 waste and friction be dissipated and human welfare 
 maintained. 
 
 Industrial growth today is determined by the busi- 
 ness man. His responsibilities to society are large 
 and his opportunities great. If he accepts the scien- 
 tific approach to his problems, is fearless enough to 
 scrap his prejudices, and at the same time construc- 
 tive enough to observe the facts; if he reaches impar- 
 tial conclusions on the basis of the facts, and then 
 
THE FACTS OP BUSINESS 13 
 
 applies them honestly to his problems, one need have 
 no fear in leaving the directive power in his hands. 
 If he is timorous, cringing, intellectually inert, and 
 oblivious to the facts of industry, then industrial 
 society must be recreated. 
 
 An outUne view of the facts with which the busi- 
 ness executive must be famUiar, and the meaning and 
 application of which he must sympathetically under- 
 stand, is given below. No attempt is made to contrib- 
 ute a complete catalog, nor to furnish a classification 
 which will meet all of the needs of every business, but 
 only to supply under classified heads the outstanding 
 and basic facts of business. 
 
 Labor Facts: 
 
 Wages, wage-rates and earnings. 
 
 Hours. 
 
 Union membership, and types. 
 
 Strikes and lockouts 
 
 Accidents. 
 
 Compensation, Industrial and Health Insurance. 
 
 Unemployment. 
 
 Turn-over. 
 
 Immigration. 
 
 Capital Facts: 
 Capitalization. 
 Resources. 
 Earnings. 
 
 Production Facts: 
 Agricultural crops. 
 Raw materials extracted. 
 Manufactures. 
 Stocks on hand. 
 
 Population Facts: 
 
 Geographical distribution. 
 
 Occupations. 
 
 Earnings. 
 
14 STATISTICS IN BUSINESS 
 
 Market Facts: 
 Money. 
 Banking. 
 Credit. 
 Trade. 
 
 Commodity prices. 
 Security prices. 
 Competition. 
 Failures. 
 Forecasting. 
 
 Land and Building Facts: 
 Land and building values. 
 Taxes. 
 Restrictions on use. 
 
 Transportation Facts: 
 Foreign rates and fares. 
 Foreign facilities. 
 Domestic rates and fares. 
 Domestic facilities. 
 Domestic control. 
 
 Law and Policy Facts, as expressed through law and the activi- 
 ties of 
 State Railroad and Utility Commissions. 
 State Tax Commissions. 
 State Industrial Commissions. 
 Federal Trade Commission. 
 United States Department of Agriculture. 
 Unted States Geological Survey. 
 Interstate Commerce Commission. 
 United States Tariff Commission. 
 
 It is not enough, however, simply to appreciate that 
 these facts have business significance. It is necessary 
 to know where the data bearing on each of the various 
 subjects may be secured, to know something of their 
 pecuUarities, and to be able to use them in connection 
 with the problems which currently arise. 
 
 The following bibliographical comments have refer- 
 ence only to the major sources of business facts, and to 
 
THE FACTS OF BUSINESS 15 
 
 some of the more evident criticisms which might be 
 made of them. Both the sources and the cautions 
 are significant more as a general than as a detailed 
 statement. 
 
 Labor Facts 
 
 For business, as a whole, no single source of data on 
 labor facts is superior to the publications of the United 
 States Bureau of Labor Statistics, and no single publi- 
 cation of this bureau is more significant than the 
 Monthly Labor Review. This publication contains 
 literally a mine of information, discriminately col- 
 lected and issued in such form as to meet many of the 
 needs of business with respect to general and detailed 
 labor facts. 
 
 Wage-rates and Earnings. — Particularly is the 
 above publication significant in the presentation of 
 wage and wage-rate data for the larger industries, and 
 for union labor. The wage and wage-rate data are as 
 nearly comparable as they can be made for different 
 times and for different types of enterprises. They are 
 supplied not only in the form of actual rates, in 
 which distinction is made for regular, overtime, and 
 specialized conditions, but are reduced to a compara- 
 tive or index number basis, so as to be of service for 
 historical comparisons. The publication does not 
 regularly contain wage-rates for non-union labor. 
 However, from time to time, wage data are given on 
 non-union employees, and from them a comparative 
 picture, at least for a few industries, may be secured. 
 
 Union Membership and Types. — The Monthly 
 Labor Review, reports of the New York Industrial Com- 
 mission, and the Annual Report of the Proceedings of 
 
16 STATISTICS IN BUSINESS 
 
 the American Federation of Labor contain data on union 
 membership, types of organization, union agreements, 
 and other union activities. 
 
 Strikes and Lockouts. — Similarly, data on strikes 
 and lockouts are published in the Monthly Labor Re- 
 view. The data are secured, for the most part, from 
 union secretaries and others who are in a position to 
 know the facts, and are reduced to a comparable 
 basis for important industries and for great industrial 
 centers. 
 
 Accidents. — Statistics of industrial accidents are 
 also published in the Monthly Labor Review, in a com- 
 prehensive way, through special studies growing out 
 of the Bureau's surveys, and in compilations of acci- 
 dent experience, as reflected in hazardous industries. 
 The steel industry has been given particular atten- 
 tion in this respect. Moreover, the Review regularly 
 summarizes the legislation having to do with acci- 
 dents and their compensation, with the rules governing 
 the installation and use of safety devices, etc. 
 
 Compensation, Industrial and Health Insurance. 
 The Monthly Labor Review regularly contains dis- 
 cussions of compensation, as well as industrial and 
 health insurance, and gives the statistics that are 
 significant on these subjects. The business man, in 
 these days of liability for accidents and industrial dis- 
 ease, cannot afford to be unacquainted with these 
 facts, as here summarized, and with the developments 
 in these important industrial fields. 
 
 Unemployment. — From the standpoint of the in- 
 dividual, and of industry as a whole, unemployment 
 is a serious problem. It represents an economic waste 
 from the standpoint of the person unemployed, and 
 
THE FACTS OF BUSINESS 17 
 
 is proof of industrial mal-adjustment for industry as a 
 whole. Unemployment data, secured from the larger 
 industrial centers and employers, and from union 
 records, are periodically published in the Monthly 
 Labor Review. They serve as a basis for measuring the 
 state of the labor market and the source of labor sup- 
 ply. In this field, the publications of the New York 
 Bureau of Labor and of the Massachusetts Industrial 
 Commission, are significant. 
 
 Labor Turn-over. — ^Labor turn-over in industry is 
 a problem to which the business executive is finding it 
 necessary to give more of his attention. His success 
 depends upon a stable and industrious labor force, and 
 every attempt should be made to reduce the turn-over 
 to a minimum. A high labor turn-over figure repre- 
 sents a loss to the employer, and a sacrifice of wages 
 to the employee. Standards for measuring it and the 
 experience of larger industries, are fully discussed in 
 the Monthly Labor Review, and business executives 
 should be acquainted with this treatment. Figures 
 on labor turn-over are so susceptible of mis-interpreta- 
 tion, and what constitutes labor turn-over is so difficult 
 of measurement in a form to be significant, that the 
 service of the Bureau in digesting experience and es- 
 tablishing standards for the measurement, ought not 
 to be overlooked. 
 
 Immigration. — The most important single source 
 of data on immigration is the reports of the United 
 States Bureau of Immigration. Immigrant labor has 
 constituted, and will continue to constitute, an impor- 
 tant element in our labor supply. The relationship of 
 immigration to industrial development, to a fluctuat- 
 ing labor supply, to turn-over, and problems of manage- 
 
18 STATISTICS IN BUSINESS 
 
 ment, is so vital that business executives must see 
 this subject in its broader aspects, and attempt to 
 measure its application to their problems as they arise. 
 The facts on immigration are conveniently summa- 
 rized in a useful form for business in the Monthly 
 
 Labor Review. 
 
 Capital Facts 
 
 The sources of information on capital facts are 
 numerous. At five-year intervals for industrial and 
 manufacturing enterprises, the amount of capital em- 
 ployed is published in the reports of the United States 
 Census Bureau. The data are only roughly accurate 
 for separate industries, but are significant even in this 
 form as measures of business activity. 
 
 Capitalization, as distinct from capital, is also re- 
 ported for industrials, for railroads, and other types of 
 corporations, in Moody's Manual, Poor's Manual, etc. 
 The data from these sources are given for individual 
 enterprises, rather than for industries as a whole, and 
 business should be thoroughly familiar with them. 
 Similarly, the capitalization of corporations and other 
 forms of business enterprise, is given in annual re- 
 ports, and in the financial prospectuses issued by 
 investment houses at the time loans are made and 
 securities underwritten. 
 
 Resources. — The resources of corporate and other 
 enterprises are described in detail in such financial 
 pubHcations as Moody's Manual, Poor's Manual, etc. 
 These publications should be on the desks of business 
 executives and constantly referred to in matters af- 
 fecting credits, investments, etc. 
 
 Earnings. — The earnings of industrial and other 
 enterprises are, of course, the most single significant 
 
THE FACTS OF BUSINESS 19 
 
 fact in relation to business promotion and success. 
 Earnings, as reported, are often deceptive. So much 
 depends upon the interpretation of the term, the con- 
 ditions under which the figures are measured, and the 
 periods to which they apply, that discrimination is 
 needed in the interpretation of the figures supplied, no 
 matter what the source of the data is. For these facts, 
 in relation to industrial enterprises, not especially sub- 
 ject to public regulation, recourse must be had to 
 financial journals, such as Bradstreet's and Dun's. 
 For railroads and public utilities, where regulation by 
 state or federal authority is the rule, and where uni- 
 form systems of accounts prevail, earnings as pub- 
 lished may in a more accurate sense be considered 
 authoritative. 
 
 Production Facts 
 
 Crops. — The United States Department of Agri- 
 culture regularly and periodically supplies facts con- 
 cerning crop production, crop condition, crop prices, 
 etc. Particularly worthy of mention as bearing on 
 these problems, is the Monthly Crop Report. This re- 
 port gives estimates for the main crops on acreage, 
 prices, total production, acreage production, and 
 similar subjects. Special reports are periodically 
 made on crop production, and intensive studies are 
 published from time to time on other important 
 agricultural problems. 
 
 Raw Materials Extracted. — The primary source 
 of information on extraction of raw materials, is the 
 Geological Survey. The reports from this source 
 cover oil, iron, coal, etc., and are prepared in coopera- 
 tion with state geological surveys and producers of 
 such commodities. Typical private publications hav- 
 
20 STATISTICS IN BUSINESS 
 
 ing to do with metal and mineral products are The 
 Iron Age; The Manufactures Record; The Metal Indus- 
 try; Engineering and Mining Journal; Drugs, Oil and 
 Paint; Coal Age. 
 
 Manufactures.— The United States Census Bureau 
 is the primary source of information on manufactures. 
 The reports cover capital invested, raw materials used, 
 wages paid, number of employees, etc., for practically 
 all of the important industries of the United States. 
 A five-year census is taken, and reports are issued by 
 industries and by states. From these data, bulletins 
 are published at intervals so that it is possible to make 
 an industrial picture of the country, and to measure 
 the development which takes place in each of the in- 
 dustries covered. Many of the data are Uttle better 
 than carefully prepared estimates, but are of distinct 
 service to business executives and others upon whom 
 the problems of industry rest. Typical private pub- 
 lications dealing with manufactured products are India 
 Rubber World; The Leather Manufacturer; Fiber and 
 Fabric. 
 
 Population Facts 
 
 Geographical Distribution. — The geographical dis- 
 tribution of the population of the United States is 
 shown in the reports of the United States Census 
 Bureau at its decennial census. These data furnish 
 measures of population concentration, migration, and 
 growth, and, if carefully interpreted, may be used in 
 estimating the buying power of different markets. 
 Taken in connection with the Bureau's report on Occu- 
 pations, and the reports of the Treasury Department 
 on internal revenues and income taxes, and with the 
 reports of the Bureau of Agriculture, these data may 
 
THE FACTS OF BUSINESS 21 
 
 serve as a basis for sales and advertising campaigns, 
 
 for the study of the localization of industry, and other 
 
 industrial purposes. The data are only roughly 
 
 accurate, but rough accuracy is all that is demanded 
 
 in this case. 
 
 Market Facts 
 
 Money. — The facts concerning the circulation of 
 money and the production of precious metals, are 
 contained in the federal government's reports issued 
 by the Treasury Department, the Comptroller of the 
 Currency, the Federal Reserve Board, etc. 
 
 Banking. — Data on banking activities are regularly 
 issued by the Federal Reserve Board in its Bulletin, 
 and by the different state bank commissioners, and 
 are summarized conveniently for the business man in 
 such private publications as The Commercial and 
 Financial Chronicle; Dun's Review; Bradstreet's and The 
 Annalist. The resources and Uabilities of the United 
 States banks are included in the reports of the Federal 
 Reserve Board, and those of the state banks in the re- 
 ports of the various state bank commissioners. 
 
 Credit. — Comprehensive facts concerning credit are 
 to be had from the private publications named in the 
 paragraph above, and in the daily press where market 
 data on loans, interest rates, clearings, domestic and 
 foreign exchange rates, etc., are published. 
 
 Trade. — The most satisfactory source of trade data 
 is the Monthly Summary of Commerce and Finance, 
 issued by the Department of Foreign and Domestic 
 Commerce, Washington, D. C. In this publication, 
 exports and imports are given in detail, both as to 
 quantities and as to value. This pubhcation, to- 
 gether with the daily and other reports of consular 
 
22 STATISTICS IN BUSINESS 
 
 agents, should be a common source of information to 
 which business men should turn for data on this phase 
 of their business activities. 
 
 Commodity Prices. — Data on commodity prices are 
 published regularly by the financial journals, such as 
 Bradstreet's; The Annalist; etc., but are most conven- 
 iently and authoritatively compiled by the United 
 States Bureau of Labor Statistics, and published in 
 the Monthly Labor Review. This publication includes 
 both wholesale and retail prices, and gives both the 
 actual and relative prices for goods which enter into 
 a consumer's budget, and into the process of produc- 
 tion. This pubHcation compiles both whoesale and 
 retail price index numbers, and, as nearly as is possible, 
 supplies a barometer of price condition and change 
 for the United States. Commodity prices are also 
 included in a great number of private publications, 
 such as The Iron Age; Drugs, Oils and Paints; Fiber 
 and Fabrics. 
 
 Security Prices. — Security prices of listed and un- 
 listed securities, besides being reported in the daily 
 press, are summarized at intervals in such publications 
 as Bradstreet's; Dun's; The Annalist; The Economic 
 World. 
 
 Failures. — Statistics of financial and industrial fail- 
 ures are reported regularly by Dun's Review, and these 
 represent the best available figures for the country 
 as a whole. Failures constitute a barometer of trade 
 and business conditions, and are significant in business 
 forecasts. 
 
 Forecasting. — Statistical data of a business character 
 are used as a basis for business forecasting by the 
 Babson Service, Brookmire Service, Moody Service and 
 
THE FACTS OF BUSINESS 23 
 
 Harvard Committee on EconomicResearch. The chief 
 merit of the services issued by the Babson, Brookmire, 
 and Moody organizations consists, in the writer's 
 judgment, in the great amount of data which are 
 collected, and which are made convenient for business 
 use, rather than in the forecast which is made. These 
 services are open to criticism in the use which is made 
 of the data, and in the assumptions which are made 
 concerning business cycles; and should be used by the 
 business man rather as a relative than as an absolute 
 measure of business conditions and likely change. The 
 service now being issued by the Harvard Committee 
 on Economic Research is thoroughly scientific, and 
 seems to possess distinct merits in actual forecasting. 
 Land and Building Facts. — Statistical facts of 
 which the business man should be in possession con- 
 cerning land and building values, taxation, and re- 
 strictions on their use, can be secured by a study of 
 the reports of assessors, tax commissioners, and others 
 having to do with taxation matters. Unfortunately, 
 these facts are sometimes not available for business 
 use, and in many instances are not prepared in such a 
 way that they are of distinct service to business as 
 issued. The main facts are available, however, even 
 though they may require considerable interpretation 
 and readjustment for particular uses. 
 
 Tbanspoktation Facts 
 
 Domestic rates and fares for transportation service 
 are regularly published, under the supervision of the 
 federal government, by carriers and tariff associations. 
 At the present time, the supervision is exercised by 
 the Railroad Administration, and by the Interstate 
 
24 STATISTICS IN BUSINESS 
 
 Commerce Commission, jointly. There is no occasion 
 for the business man to be in doubt concerning trans- 
 portation charges, since the law clearly requires that 
 full publicity shall be given to them. 
 
 The reports of the Interstate Commerce Commis- 
 sion on freight and passenger movements, on wages 
 and financial conditions of transportation companies, 
 constitute a veritable mine of information, and under 
 the newly provided accounting system, will be of even 
 more distinct service than the reports have been in 
 the past. The private publications which most fully 
 cover transportation facts are the Railway Age Gazette, 
 and Poor's Manual, and the reports of the Bureau of 
 Railway Economics, Washington, D. C. 
 
 Law and Policy Facts as Expressed Through Law, 
 
 AND THE Activities op State and Federal 
 
 Boards and Commissions 
 
 The results of the operations of public utility com- 
 missions, and other state and federal boards, are cur- 
 rently summarized in their annual reports. These 
 reports, moreover, contain suggested laws, legal inter- 
 pretations, restrictions, and methods of control, with 
 which the business man should be familiar, and which 
 are fundamental to his success. These commissions 
 have to do with railroad and utility companies, tax 
 methods and measures, industrial compensation, 
 health and accident insurance, wages, trade activi- 
 ties, combinations, competition and business practices, 
 tariffs, etc. 
 
 The attitude of the government toward types of 
 business and the methods which are followed, should 
 
THE FACTS OF BUSINESS 25 
 
 be known, so far as is humanly possible. No condi- 
 tion is so detrimental to business as uncertainty. 
 Public opinion, so far as it has been crystallized, may 
 often be read in these reports, and the business man 
 must be familiar with them. 
 
 It is not intended, of course, that every business 
 executive should be familiar with all of the facts 
 suggested above, or the sources from which they may 
 be secured, but it is necessary, in so far as the problems 
 of his business extend into the fields mentioned, that 
 these and other sources of information should be 
 thoroughly known, and the data which they contain 
 be fully understood. 
 
 Many of the facts which are needed by business, in 
 order to approach its problems in a scientific manner, 
 are available in such sources as those listed above; 
 others are in process of collection; and others must 
 be secured de novo. Where these facts are, how good 
 they are, and the methods by which they may be 
 secured, are discussed in the following chapter. 
 
CHAPTER III 
 RECOGNIZING AND SECURING THE FACTS 
 
 The statement was made in the beginning of the 
 last chapter that a business fact, in order to be used 
 as the basis for a business judgment, must, among 
 other things, be definite and measurable. In this 
 chapter this point of view is given definite application, 
 and its importance illustrated by reference to con- 
 crete problems. 
 
 Every business, large or small, is daily confronted 
 by a series of problems. Some of these are current, 
 others are periodic. About the solution of them there 
 is often a degree of uncertainty, which on the surface 
 is baffling. Deeper down, however, many of them 
 may, on investigation, be found to rest upon a rela- 
 tively few major issues, and group themselves about 
 a few basic facts. Their solution may in part be 
 accomplished by a proper approach. The problems 
 may, for instance, relate to the advisability of begin- 
 ning a campaign of advertising, of increasing a labor 
 force, of more thoroughly cultivating certain sales 
 territory, as an alternative to lowering prices, or re- 
 adjusting production methods, in view of increased 
 wages and shorter hours. In what frame of mind 
 must the busines man, no matter how large or how 
 small a business he controls, meet them? • What must 
 be his attitude toward them? It cannot be one of 
 inattention and disregard. Problems have a way of 
 
 26 
 
RECOGNIZING AND SECURING THE FACTS 27 
 
 becoming cumulative, and to defer them, or to leave 
 them to self-adjustment and self-settlement, is ruin- 
 ous in the end. 
 
 Every business problem should be approached by 
 an executive with: 
 
 First, a clear and certain respect for the truth; 
 second, a desire to understand the facts and to apply 
 them whole-heartedly toward a solution of the prob- 
 lems. The first involves a point of view; the second, 
 a method of procedure. 
 
 The first two chapters have, we hope, established 
 the necessity for the application of the scientific 
 method to business problems. So much for the 
 point of view. It can now be taken for granted, and 
 the discussion proceed at once to the conditions 
 which govern its application. 
 
 A business fact, statistical or otherwise, is always 
 relative. "Success" is not absolute; neither is "fail- 
 ure." "Bumper" crops, "poor" trade, "bull" mar- 
 kets, "successful" advertising, "high" interest rates, 
 and "steady" markets, are relative expressions. The 
 statistical data which express them, although definite, 
 are not to be interpreted in an absolute sense. The 
 measurements are relative and must be appraised in 
 connection with the problems and the conditions to 
 which they apply. The relation between a problem and 
 its measurement is reciprocal; the fact ought not to be 
 divorced from the problem, and the problem cannot 
 be understood without the fact. The following ex- 
 amples of statistical facts, considered in connection 
 with concrete problems, will illustrate the meaning 
 of this truth in business affairs. 
 
 A strike is a statistical fact. It is commensurable 
 
28 STATISTICS IN BUSINESS 
 
 and may be stated numerically, as twenty during the 
 year. But not all strikes are identical. They differ 
 as to the number of laborers and others affected, size 
 of industry involved, duration, grievance, temper of 
 strikers, issues at stake, etc. The amount of gross 
 sales in dollars is another statistical fact. But two 
 sales experiences of equal gross amount may be differ- 
 ent in every other respect. One may result from an 
 intensive campaign of advertising among small towns 
 in an old field; the other, from the practice of direct 
 selling in virgin fields, with an entirely different sales 
 otganizatioii. 
 
 An industrial accident, likewise, is a statistical fact, 
 but its meaning is different for different industries, 
 size and nationality of labor force, industrial hazard, 
 conditions of operation, duration of exposure, etc. 
 The experience of the industries of one state, as 
 reflected in the number or result of accidents, is of 
 little value in another state unless the basis of enu- 
 meration is uniform and the duration of exposure is 
 expressed in a common unit. The same is equally 
 true in comparing accident frequency and accident 
 severity rates in two departments. Most of the 
 statistics of labor turn-over, when removed from the 
 particular plant or industry in which they are collected, 
 are of little comparative value. Units of measure- 
 ments are not abstract; they refer to definite and 
 measurable things. A ton, for instance, is invariably 
 a ton; but all tons, except as to weight, are not the 
 same. The problem of enumeration is not so much 
 that of counting the same thing, as it is of counting 
 different things which are given the same general 
 name; things which are equal to each other in name 
 
EECOGNIZING AND SECURING THE FACTS 29 
 
 are often not so in use. Facts must be standard- 
 ized, and standardization implies homogeneity; it 
 suggests suitability to conditions required in the light 
 of particular application. The meaning of a business 
 fact is a function of the use to which it is put. 
 
 The point which is being made is that the meaning 
 and use of business facts cannot be dissociated. The 
 scientific method requires that problems be broken up 
 into their various parts, that these be measured by 
 homogeneous units, and that comparisons rest upon 
 common qualities. Comparisons are invalid, and 
 fact analysis useless for business purposes in the 
 degree to which this truth is ignored. 
 
 The tests by which a fact may be appraised as a 
 basis for a business judgment, are suggested by the 
 uses to which they are to be put. If crude compari- 
 sons only are wanted, imperfect facts will suffice. 
 Trade buoyancy may be measured for general pur- 
 poses by the amount of exports, imports, or bank 
 clearings, or by orders for steel or some other basic 
 commodity. But individual business policies, and 
 the way in which they should be adjusted to meet 
 specific problems, can hardly be based upon such 
 general figures. Not that it is unimportant in busi- 
 ness to understand trade movements and to observe 
 the fundamental tendencies in trade, finance, labor 
 and production. All these are significant, but how 
 fully an individual business may profit or suffer from 
 them can be determined only by a business analysis 
 of the particular problems with which it is concerned. 
 A nicety of discrimination is required both in diag- 
 nosing particular business ailments and in prescribing 
 the remedies for them. Only rarely can business 
 
30 STATISTICS IN BUSINESS 
 
 judgments safely rest on crude approximations. 
 Business is being conducted on narrow margins of 
 profits. The source of profits, the responsiveness of 
 customers to price policies, and the ways in which 
 cooperation and interest on the part of labor may be 
 secured can be determined only through business 
 analysis. Analysis involves comparison, and com- 
 parison requires the establishment and use of standards. 
 These can rarely be of a general character. 
 
 Without attempting here to set up standards 
 for specific types of business facts, since each fact 
 must be interpreted in connection with the prob- 
 lem to which it relates, it may be helpful to enu- 
 merate briefly the conditions which are of universal 
 application. 
 
 As a basis for comparison and application of scientific 
 method, statistical facts must, first, be homogeneous. 
 Characteristics which are significant for the purposes 
 for which the facts are to be used, should not be 
 ignored. For instance, men and women should be 
 differentiated in wage comparisons; town and city 
 population, in developing sale campaigns; religious 
 persuasions, frequently, in estimating buying power. 
 To consider a market without distinguishing con- 
 sumers' buying power, their personal peculiarities or 
 their incomes would be equivalent to treating as homo- 
 geneous that which is clearly diversified. Differences 
 of training, psychological behavior, standards of 
 livelihood and tastes are all significant in shaping 
 selling policies. People are homogeneous as to com- 
 paratively few characteristics. The business man 
 who conceives of his problems scientifically will take 
 note of all differences which are significant from the 
 
RECOGNIZING AND SECURING THE FACTS 31 
 
 point of view from which he proceeds. Comparisons 
 between the turn-over of goods may be misleading if 
 this requirement is forgotten. The turn-over figure 
 for one type of merchandise can not be accepted for 
 another. The market price which would discourage 
 sales in one field acts as no deterrent in another. 
 Labor, too, is non-homogeneous. In a general labor 
 turn-over figure are represented casual and responsible 
 labor services. To replace some, costs are negligible; 
 to replace others, costs are prohibitive. Comparisons 
 must be made between things having common qualities, 
 regard always being had to the purposes in mind. 
 Violation of this principle leads to imperfect generali- 
 zations and false conclusions. 
 
 Second, statistical facts must be representative. Un- 
 representative facts, due either to ignorance or to 
 conscious design, are an uncertain basis upon which 
 to base a business judgment. Where bias rules, the 
 occasion for error exists. When the motive to deceive 
 is present, little difficulty is encountered in making a 
 case. Bias may be due to wilfully eliminating part 
 of the facts, to basing conclusions on insufficient data, 
 or to comparing periods or conditions that have noth- 
 ing in common. Truth is desired, and every effort 
 must be made to attain it. It is the function of the 
 facts to reveal truth, not to conceal or distort it. 
 
 In market analysis by sampling, the question is 
 always important : Are my samples representative or is 
 there bias running through them due to selecting too 
 narrow a territory, too small a group or too restricted 
 a class? Statistical principles require that every 
 sample must contain the characteristics of the group 
 and that these be represented in proportion to their 
 
32 
 
 STATISTICS IN BUSINESS 
 
 presence in the original data. Cost of living data 
 selected from one economic strata will hardly suffice 
 to determine a disputed wage adjustment for another 
 group whose incomes are different. For instance, the 
 amount and per cent, of expenditure for food for 
 12,096 white families in 92 industrial centers varies 
 for each income group as follows :' 
 
 Table 1. — Amount and Per Cent, op Expenditures fob Food by 
 Income Groups 
 
 
 
 
 Average yearly expenditure 
 
 Inoome groups 
 
 Number of 
 families 
 
 Equivalent 
 adult males 
 
 
 
 Amount 
 
 Per cent. 
 
 Total 
 
 12,096 
 
 3.33 
 
 8548.50 
 
 38.2 
 
 Under $900. .. 
 
 332 
 
 2.89 
 
 371.61 
 
 44.1 
 
 $900 to 1200. . . 
 
 2,423 
 
 2.98 
 
 456.16 
 
 42.4 
 
 1200 to 1500... 
 
 3,959 
 
 3.16 
 
 515.55 
 
 39.6 
 
 1500 to 1800... 
 
 2,730 
 
 3.36 
 
 571.75 
 
 37.2 
 
 1800 to 2100... 
 
 1,594 
 
 3.62 
 
 626.52 
 
 35.7 
 
 2100 to 2500... 
 
 705 
 
 4.09 
 
 711.86 
 
 34.6 
 
 2500 and over.. 
 
 353 
 
 4.95 
 
 859.98 
 
 34.9 
 
 And yet, is it not a common practice not only to 
 ignore the relationship of expenditure to income, but 
 also to identify expenditures for food, rent, clothing, 
 etc., with the "cost of living" to any group irrespective 
 of the standard which they maintain? How com- 
 pletely is the "cost of living" represented in the retail 
 price changes of the 22 commodities used by the 
 United States Bureau of Labor Statistics? "Cost of 
 living " to whom? How representative of market con- 
 
 1 Monthly Labor Review, United States Bureau of Labor Statistics 
 August, 1919, p. 118. 
 
RECOGNIZING AND SECURING THE FACTS 33 
 
 ditions are the 25 wholesale price changes weekly 
 shown by the New York Annalist? 
 
 Again, how nearly is the stock and bond market 
 gauged by the average price of 25 industrial stocks or 
 25 railroad bonds? Are the selected securities repre- 
 sentative, and what effect on the result comes from 
 taking an average (arithmetic mean) when a large 
 change in a single security may influence the result as 
 much as minor changes in a number of securities? 
 Moreover, what condition or personal interests are 
 held in mind in deciding whether they are "represen- 
 tative?" Ought not the prices to be multiplied by the 
 amount sold in order to be of interest to the speculator, 
 and multiplied by the amount outstanding to be of 
 significance to the stockholder? 
 
 Third, facts must fit the problem; they must be 
 germane. Do the facts which you employ accurately 
 describe your problem? Are they too narrow, or too 
 broad; too restricted, or too general? Are your prob- 
 lems so peculiar that the facts of trade, labor and 
 market conditions do not apply? Why? Can you 
 demonstrate the lack of application, or are you hiding 
 behind the old shibboleth, "my business is different?" 
 Be square with yourself, and scientific toward the 
 facts available. If they do not fit your business, 
 prove it, and secure those that do. Ignorantly to 
 select data at random to support a contention or to 
 develop a business policy violates both aspects of 
 scientific method. There is then neither intelligent 
 observation of facts nor logical inference from them. 
 Refer every fact to the condition which can produce it. 
 Fourth, facts must be stable. They must relate to 
 periods and conditions which are essentially uniform. 
 
34 STATISTICS IN BUSINESS 
 
 Look for the norm in your business. Business judg- 
 ments based on exceptions and on erratic conditions 
 or periods are unstable. Distinguish between the 
 short- and the long-time influences, and in analyzing 
 your business difficulties, select the facts which apply 
 to homogeneous conditions. Distinguish between 
 the facts which measure transitory skirmishes and 
 those which describe permanent tendencies. Busi- 
 ness facts are constantly changing; some fluctuate 
 rapidly, as prices of speculative securities; others are 
 more stable, as, in normal time, the rate of Sterling 
 exchange. Some changes are sporadic; others are 
 periodic. When changes are frequent, measurements, 
 to be representative, must be numerous, as for in- 
 stance in studying piece-rates in the clothing trade. 
 Where periodic changes occur, as in the movements of 
 crops, in receipts of wheat at elevator terminals, or 
 in the price of eggs, measurements should cover a com- 
 plete cycle. 
 
 Fifth, both the facts themselves, and the conditions 
 of the measurement, must be comparable. "Like can 
 only be compared with like." Shifting conditions of 
 measurement, and changing units, cannot be tolerated. 
 Use the same measuring stick and apply it in the same 
 way throughout all measurements. Profits are not 
 comparable from period to period, when definitions 
 change and the base upon which they are determined 
 shifts. Be consistent in measuring your business 
 successes and failures, and logical in the interpretation 
 of them. 
 
 Sixth, facts must be accurate. Accuracy is affected 
 by the conditions under which facts are reported and 
 collected. If they are not understood, or if their col- 
 
RECOGNIZING AND SECURING THE FACTS 35 
 
 lection incites distrust, and arouses suspicion or the 
 desire to protect oneself, inaccuracy creeps in. To 
 what extent, this is true, is often difficult, if not impos- 
 sible, to determine. Moreover, facts may be correctly 
 reported, but the report be inaccurate because they 
 have been wrongly determined. Occupations, for in- 
 stance, are confused in the absence of standardized 
 nomenclature, and the real cause of occupational 
 death is often not revealed because of amateurish 
 diagnosis, or desire to conceal the truth. Moreover, 
 facts may be inaccurate, because accuracy is impos- 
 sible to attain. The wages of farm labor, or the acre- 
 age of corn harvested within the United States, can 
 only be estimated. Estimates are all that are desired, 
 and they are all that are published. Business execu- 
 tives and others must treat them as estimates, and 
 be cognizant of the conditions under which they are 
 made. Against the imputation of gullibility, the 
 executive must always be capable of defending himself. 
 
 The facts of business for the most part grow out of 
 daily routine operations. Some are collected by 
 business organizations for their own use, some by 
 trade pubUcations, and still others by governmental 
 agencies. What the significant facts are, which are 
 hidden away in routine reports, or systematically 
 collected, it is the function of the business man to 
 know; how they apply to his problem, it is his duty to 
 understand. 
 
 In studying business facts, the executive must apply 
 both general and specific tests of worth and applica- 
 tion. In searching his own records for them, he must 
 classify his problems and apply the facts which are 
 germane. While business units operate primarily for 
 
36 STATISTICS IN BUSINESS 
 
 profit, and only secondarily, if at all, as statistical 
 laboratories in the production of facts, yet the rela- 
 tion between fact analysis and business success is so 
 close that it cannot be ignored. Statistical and re- 
 search departments cannot become a part of every 
 business undertaking, but there is no business so 
 small that it cannot duplicate in a small but effective 
 way the attitude of mind suggested by these special 
 departments. This attitude is one of business curiosity 
 and intellectual integrity toward problems as they 
 arise. 
 
 The attitude of the executive toward his business 
 affairs must be. Why? Where is the logical justifica- 
 tion of the action taken? Does custom dominate 
 the contents of my records, my reports, my office 
 organization, my advertising, the treatment of my 
 labor force? How do I stand with my competitor, 
 in the matter of costs and services? Are the resources 
 of my organization fully employed? How might I 
 use my oflSce, sales, and production records to decrease 
 costs, to analyze my markets, experiment with prices, 
 increase my capital, and decrease my labor turn-over? 
 Is my business a "going" concern, and where is it 
 "going?" 
 
 Business analysis — the application of scientific 
 method — in commercial enterprise, will answer such 
 queries, and suggest such positive action as the 
 following : How can I extend my market ? (Describe 
 your present market in terms of its possibilities.) Is 
 my sales record the best? (Establish a standard of 
 "best.") What are my selling costs? (Define costs 
 accurately and defend the amount.) What share of 
 the business in my line am I getting? (Measure and 
 
RECOGNIZING AND SECURING THE FACTS 37 
 
 localize the buying power available.) Are my salesmen 
 the best? (Establish a standard of salesmanship and 
 realize it in your own organization.) Are the reports 
 of my salesmen filled with business meaning, or are 
 they perfunctory? (Submit them to critical inspec- 
 tion, and make yourself defend them.) 
 
 A business, to be successful, must have standards 
 and be critical of them; it must eliminate the dry rot 
 which unconsciously accumulates, and accept the 
 truth, that progress means change, but change only as 
 the result of conscious, purposeful choice. Beware 
 of innovations as such — the gold bricks of success — 
 but welcome and cultivate improvement through 
 positive change. 
 
 The facts which are needed for the solution of many 
 business problems exist in whole, or in part, in the 
 daily records which are kept. When they are not 
 currently collected, they must be secured. It may be 
 necessary in large establishments to create separate 
 departments to secure and interpret them; in others 
 it may require nothing more than the interest and 
 talents of a single individual. Business does not 
 hesitate to adopt the specialized machinery of produc- 
 tion; it must not hesitate to install suitable machinery 
 for the collection and interpretation of business facts. 
 To determine what these are, where they are, how 
 they may be collected, what they mean, and how they 
 may be applied in the solution of business problems, 
 constitute the essence of fact analysis. 
 
 A serious weakness of business is to allow the 
 problem of office organization, accounting readjust- 
 ments, etc., to drift. In many instances, the changes 
 and modifications which are essential to secure 
 
38 STATISTICS IN BUSINESS 
 
 economy and to increase output are not known. 
 This may be due to wilful ignorance, or more often, 
 probably, among smaller business units, to lack of 
 facilities for keeping in touch with modern develop- 
 ments and progress touching these matters. The 
 latter condition, by means of advertising and other 
 educational methods, wiU sooner or later be dispelled 
 for all but a fraction of establishments. There is not 
 so much hope, however, for the wilfully ignorant — 
 for the individual who "knows it all," and at the same 
 time knows little or nothing beyond the routine of his 
 daily grind. Concerning this individual, hope lies 
 primarily not in education, but in elimination. 
 Sooner or later he must give way. His goods and 
 services, coming at too great a cost, are lost to the 
 market, and justly so. Competition slowly forces 
 him out, but only after the social costs have become 
 intolerable. He or his like reappears, however, be- 
 cause of the unequal advantages under which industry 
 is carried on — there is a sort of perpetual handicap 
 for some running throughout all industry. It may, 
 however, be lessened by business self-analysis. Where 
 the disposition to make this analysis does not exist, 
 and where the justification for not making it is sought 
 in a self-centered complacency, the problem is hopeless. 
 More often, however, lack of progress is due not so 
 much to wilful ignorance as it is to the absence of a 
 scientific approach to business problems. An execu- 
 tive may be open to suggestion; he may be willing to 
 adopt labor- and time-saving devices, and may have 
 caught the social point of view respecting problems 
 of labor. He may also approach market problems 
 from the standpoints of psychology and of the new 
 
RECOGNIZING AND SECURING THE FACTS 39 
 
 competition and upon the basis of analysis of popula- 
 tion and occupational data. But still there may be 
 something lacking in his attitude — something that is 
 vital to the application of the scientific method. 
 What too many progressive business executives fail 
 to realize is that the scientific method, or fact analysis, 
 is not to be applied sporadically; is not to be apphed 
 here and neglected there; begun and then allowed to 
 lapse. For an executive to appreciate the meaning 
 of fact analysis is not enough. He must create and 
 maintain an organization to apply it. It must become 
 a religion not only to him, but to the others in his 
 industry as well. Simply to order sales to be analyzed, 
 or a new acounting control to be established, without 
 at the same time providing the ways in which it 
 shall be done, and allowing for all of the consequences 
 which will follow, is only to catch a glimpse of the 
 meaning of scientific method. Glimpses alone are not 
 enough; conviction is what is needed, and this must be 
 general and felt by all those on whom responsibilities 
 rest. The lesser oflBicials, the department managers, 
 and even the workers themselves, are the ones who 
 are in a position to see the need for fact analysis; and, 
 if convinced of its services, can be of inestimable ser- 
 vice to the management in suggesting improvements 
 to be made and in observing the results of the changes 
 introduced. The technique of scientific method will 
 have to be applied by the expert, but he should have 
 not only the sympathy but also the cooperation of all 
 those in whom any responsibility rests. An esprit de 
 corps is indispensable. 
 
 Scientific method has been defined as a state of 
 mind, and this is probably a true characterization if 
 
40 STATISTICS IN BUSINESS 
 
 the condition is added, that the point of view it repre- 
 sents is consistent in seeking the truth and being 
 guided by facts not at one time, in one place or under 
 one condition, and ignoring them when it becomes ad- 
 vantageous, or when they are difficult to determine, 
 but in all places, at all times, and under all conditions. 
 Cost accountants, statisticians, and industrial engi- 
 neers, in the study of business, are continually finding 
 conditions which are deplorable; where every princi- 
 ple of scientific method is violated, and where businesses 
 are running on without cost figures, depreciation re- 
 serves, sales analysis, and comparative and basic 
 operating data. A remedy is sought at the hands of 
 the expert, but only for certain specific ills, and not for 
 a complete constitutional treatment. Changes are 
 introduced with fear and hesitancy, doubt character- 
 izing every innovation. 
 
 This is not the spirit of scientific method. To the 
 fact analysist, facts are facts. They are welcomed for 
 the truth they contain. The attitude toward them 
 and toward the changes which they make imperative, 
 is positive, receptive, and open minded; not negative, 
 doubtful and hesitant. It is not a little truth, but 
 the whole truth, which is wanted. Nothing is too 
 sacred, too old, nor too customary to be challenged. 
 Truth ff om whatever source is sought out and wel- 
 comed, and applied to problems as they arise. 
 
CHAPTER IV 
 CLASSIFYING AND TABULATING THE FACTS 
 
 Business analysis involves the classification of facts, 
 the application of them to business problems, and the 
 formation of business judgments. The methods of 
 classifying facts and of presenting them in tabular 
 form are treated in this chapter. The following chap- 
 ter is concerned with the principles and rules of 
 graphic presentation. 
 
 Business phenomena and the data bearing upon 
 them must be classified. Business judgments which 
 call for more than nominal consideration, are made 
 on the basis of some sort of analysis. The pros and 
 cons are considered, given their appropriate weight, 
 and a final determination made. Decisions must be 
 reached and actions taken. Upon what basis are 
 decisions made? How soberly are the facts consid- 
 ered; is their use scientific? 
 
 Classification consists in separating facts according 
 to a definite plan, into groups, according to certain 
 characteristics, and of placing them in tables, and in 
 graphic or other form, for the purpose of presentation. 
 It presupposes a definite knowledge of the purpose 
 for which facts are studied, and the manner of pres- 
 entation depends upon the ease with which data, as 
 classified, may be understood. Sometimes tabula- 
 tion suffices, and is easily understood. In other 
 cases, some form of graphic expression is indispensable. 
 
 41 
 
42 
 
 STATISTICS IN BUSINESS 
 
 The advantages of clearly defined and logically 
 constracted tabulation forms are many. Tables sys- 
 tematize data and show the order of arrangement. 
 They make it possible to show group relations and 
 bring out comparisons. They facilitate addition and 
 summarization, and avoid the necessity of repeating 
 headings and of duplicating items. In short, they are 
 a means of recording in permanent form the analysis 
 that is made through classification and of placing in 
 juxtaposition things that are similar and should be 
 compared. How true this is may be seen by com- 
 paring the following methods of showing the number 
 of occupational deaths among cotton mill operatives 
 in Fall River, 1905-1912. 
 
 "The recorded number of male operative decedents in Fall 
 River for the eight-year period (1905-1912) was 915. Of these 
 233 . . . were found not to have been cotton-mUl operatives, 
 while 207, who on their death certificates were assigned to other 
 occupations, were really cotton-null operatives at the time of 
 their death. The real number of male operative decedents, 
 therefore, was 889, the group as recorded having been larger by 
 26 than the facts justified. 
 
 Table 2. — Occupational Deaths — Cotton-mill Operatives in 
 Fall River por Period, 1905-1912 
 
 Occupational deaths — cotton-mill operatives 
 
 Male 
 
 Female 
 
 Total 
 
 889 
 
 936 
 
 
 
 Recorded number 
 
 915 
 -233 
 207 
 
 -26 
 
 548 
 
 
 — 71 
 
 Operatives not included 
 
 459 
 
 
 +388 
 
 
CaLASSIPYING AND TABULATING THE FACTS 43 
 
 "On the other hand the recorded number of female operative 
 decedents in Fall River for the eight-year period was 548. Of 
 these 71 . . . were found not to have been cotton-mill operatives, 
 while 459, who were recorded either as having other occupations 
 or no occupation at all, proved on investigation to have been 
 really cotton-mill operatives. This gives a total of 936 decedent 
 female operatives." ' 
 
 In order to tabulate statistical data, they must 
 generally be prepared for this purpose. Sometimes 
 the units can be transferred directly into prepared 
 tables from reports, memoranda, and such sources. 
 In most instances, however, they have to be tran- 
 scribed, rearranged, combined, coded, etc., before 
 this process begins. Whether taken from secondary 
 sources, or collected from business records, they are 
 still raw material, and consistency in classification is 
 indispensable. The identity of the facts included 
 must be as complete as possible. A table is no better 
 than the classification that it expresses. 
 
 In tabulating statistical data, strive for simplicity. 
 Make tables simple in outline and their purpose 
 evident. Avoid too complex tabular arrangements, 
 and place in immediate relationship the facts which 
 are to be compared. The order in which the data 
 appear should be natural, emphatic, and convincing. 
 
 The following table shows the form in which the 
 municipal offerings of a Chicago investment house 
 were distributed to the public. The investor is prob- 
 ably most interested in the "net" return — ^notice 
 the order in which the issues are listed. The purpose 
 of the arrangement is clear. 
 
 ' Monthly Review, United States Bureau of Labor Statistics, July, 
 1917, pp. 7-8. 
 
44 STATISTICS IN BUSINESS 
 
 Table 3. — Bonds fok Safe Investment 
 
 Amount 
 
 Name of issue 
 
 Rate 
 
 Maturity 
 
 Price 
 
 and 
 
 interest 
 
 Netting 
 about 
 
 $30,000 
 60,000 
 20,000 
 
 100,000 
 
 Buffalo, N. Y., Kegistered.. . 
 
 Camden County, N. J 
 
 New York City, Registered. . 
 
 St. Louis, Mo., Bd., of Ed. 
 
 School 
 
 iH. 
 
 5 
 
 4 
 
 4 
 
 5 
 
 4 
 
 4 
 
 4?4 
 
 6 
 
 5 
 
 5 
 
 5}i 
 5 
 5 
 5 
 
 5 
 
 Nov. 2, 1934 
 Aug. 1, 1925 
 Nov. 1, 1956 
 
 July 1, 1939 
 Nov. 1, 1928 
 July 3, 1933 
 Feb. 1, 1920 
 Oct. 29, 1939 
 Oct. 24, 1939 
 Oct. 29, 1939 
 July 1, 1921 
 
 Dec. 1, 1931 
 Oct. 29, 1959 
 July IS, 1949 
 Oct. 29, 1949 
 
 1929 to 1941 
 
 102.78 
 103.10 
 92.71 
 
 94.75 
 103.75 
 94.92 
 99.75 
 100.99 
 101 .30 
 102 .37 
 100.57 
 
 105 .86 
 101.00 
 100.00 
 100.00 
 
 100.00 
 
 4.25 
 4.40 
 4.40 
 
 4.40 
 
 34,000 
 
 
 4.50 
 
 20,000 
 10,000 
 90,000 
 50,000 
 100,000 
 
 California, State Highway. . . 
 Cook County Forest Reserve 
 
 Ogden, Utah, School 
 
 Fremont, Neb., Refunding. . 
 
 4.50 
 4.50 
 4.62 
 4.70 
 4.70 
 
 10,000 
 
 Seattle, Wash 
 
 4.70 
 
 40,000 
 
 Miami Conservancy District, 
 Ohio 
 
 4.8S 
 
 200,000 
 
 200,000 
 
 15,000 
 
 30,000 
 
 Polk County, Terns, Road. . 
 Blount County, Tenn., Road 
 Denton County, Texas, Road 
 Hill County, Texas, Road 
 Dist 
 
 4.87 
 5.00 
 5.00 
 
 5.00 
 
 
 
 
 Contrast the following tables, so far as order of 
 arrangement is concerned. 
 
CLASSIFYING AND TABULATING THE FACTS 45 
 
 Table 4. — United States Ceop Estimated Prodtjction 
 August 1, 1919' 
 
 Crops 
 
 Production 
 
 1919 
 
 indicationa, 
 
 Aug. 1 
 
 Corn, bushels 
 
 Winter wheat, bushels 
 
 Spring wheat, bushels 
 
 All wheat, bushels 
 
 Oats, bushels 
 
 Barley, bushels 
 
 Rye, bushels 
 
 Buckwheat, bushels 
 
 Potatoes, bushels 
 
 Sweet potatoes, bushels 
 
 Flaxseed, bushels 
 
 Bice, bushels 
 
 Tobacco, pounds 
 
 Hay (all), tons 
 
 Cotton, bales 
 
 Apples, total crop, bushels. . . . 
 
 Peaches, bushels 
 
 Pears, bushels 
 
 Kafirs, etc., 6 states, bushels. 
 Peanuts, bushels 
 
 Beans (dry), 6 states, bushels 
 
 Sugar beets, tons 
 
 Broom corn, 5 states, tons. . . 
 
 Sorghum, sirup, gallons 
 
 Hops, pounds 
 
 2,788,378,000 
 715,301,000 
 225,080,000 
 940,381,000 
 
 1,266,401,000 
 
 203,525,000 
 
 84,552,000 
 
 16,103,000 
 
 357,120,000 
 
 100,456,000 
 
 10,239,000 
 
 43,427,000 
 
 1,335,052,000 
 
 110,876,000 
 
 11,016,000 
 
 155,004,000 
 49,793,000 
 12,260,000 
 
 130,153,000 
 57,547,000 
 
 12,338,000 
 
 6,963,000 
 
 59,100 
 
 33,757,000 
 
 34,906,000 
 
 * Monthly Crop Report, United States Department of Agriculture, 
 August, 1919. 
 
46 
 
 STATISTICS IN BUSINESS 
 
 Table 5. — Production of Corn in the Leading Five States, 
 
 1916-1918' 
 (000 omitted) 
 
 1918 
 
 1917 
 
 1916 
 
 State 
 
 Produc- 
 tion 
 Bushels 
 
 Per 
 cent. 
 
 of 
 U.S. 
 
 State 
 
 Produc- 
 tion 
 Bushels 
 
 Per 
 cent. 
 
 of 
 U.S. 
 
 State 
 
 Produc- 
 tion 
 Bushels 
 
 Per 
 
 cent. 
 
 of 
 
 U.S. 
 
 U.S. 
 
 2,582,814 
 
 100.0 
 
 U.S. 
 
 Ill 
 
 Iowa . . . 
 Nebr... 
 
 Mo 
 
 Ind ... . 
 
 5 States 
 
 3,065,233 
 
 100.0 
 
 U. S. 
 
 Iowa 
 
 111 
 
 Nebr... 
 
 Ind 
 
 Mo 
 
 5 States 
 
 2,566,927 
 
 100.0 
 
 Iowa 
 
 Ill 
 
 Ind 
 
 Mo 
 
 Ohio 
 
 375,624 
 351,450 
 169,554 
 133,860 
 133,200 
 
 14.5 
 13.6 
 6.6 
 5.2 
 5.2 
 
 418,000 
 410,700 
 249,480 
 241,500 
 196,776 
 
 13.6 
 13.4 
 8.1 
 7.9 
 6.4 
 
 366,825 
 300,900 
 192,400 
 174,658 
 132,112 
 
 14.3 
 11.7 
 7.6 
 6.8 
 5. 1 
 
 5 States 
 
 
 45.1 
 
 
 49.4 
 
 
 45.4 
 
 There is no particular sacredness about any order 
 in tabulation, unless it is the alphabetical. The order 
 should generally be chosen so as to emphasize the 
 classification which is adopted. An unnatural or 
 rule-of-thumb arrangement is never justified. 
 
 What seems to be the basis of arrangement of the 
 details in Table 6, showing the classification of 
 statistics of corporate incomes in 1916, as published 
 by the Commissioner of Internal Revenue? 
 
 Tables 2, above, and 7, following, illustrate what 
 may, for convenience, be called "Progress" tables. 
 
 In the clearest way possible project onto a tabular 
 form the message which is wished to be conveyed. 
 Make the totals prominent by placing them first, 
 and show the relative importance of the classifica- 
 tion by the rulings and the spacings of major and 
 
 1 Monthly Crop Report, United States Department of Agriculture 
 
CLASSIFYING AND TABULATING THE FACTS 47 
 Tablr 6. — ^United States Corporate Income Statistics, 1916* 
 
 1916 Classification 
 
 Class 
 
 Net inoome 
 
 Total 
 
 $8,765,908,984 
 
 
 Banks 
 
 400,599,580 
 
 127,906,231 
 
 1,541,076,130 
 
 798,883,349 
 
 Insurance companies 
 
 Public utilities 
 
 Extraction of minerals 
 
 Manufacturing and mechanical 
 
 4,157,625,900 
 464,875,807 
 
 Merchandising 
 
 Agriculture and animal husbandry 
 
 69,862,431 
 
 Miscellaneous 
 
 1,205,079,556 
 
 
 
 Table 7. — Live Stock Changes dtjrinq July * 
 
 Cattle 
 
 1919 1918 
 
 Swine 
 
 1919 1918 
 
 Sheep 
 
 1919 1918 
 
 On farms July 1 
 
 Births in July 
 
 Brought on farms in July 
 Moved off farms in July. 
 Farm slaughter in July. . . 
 
 Died on farms in July 
 
 Remaining Aug. 1 
 
 100.00 
 
 2.78 
 
 1.53 
 
 4.97 
 
 .29 
 
 .34 
 
 98.71 
 
 100.00 
 
 3.19 
 
 2.99 
 
 6.01 
 
 .49 
 
 .45 
 
 99.23 
 
 100.00 
 7.88 
 1.79 
 8.48 
 .30 
 1.79 
 99.10 
 
 100.00 
 
 9.86 
 
 2.16 
 
 11.31 
 
 .45 
 
 1.68 
 
 98.58 
 
 100.00 
 .38 
 .63 
 4.80 
 .44 
 .81 
 94.86 
 
 100.00 
 
 .38 
 
 2.14 
 
 6.85 
 
 .60 
 
 .87 
 
 95.20 
 
 minor headings. Make tables attractive, concise, 
 and emphatic. Fit them appropriately to standard 
 sized pages; number the lines and columns when this 
 will result in clarity; and above all give them suitable, 
 
 ' American Economic Review, September, 1919, p. 512. 
 
 2 Monthly Crop Report, United States Department of Agriculture. 
 
48 
 
 STATISTICS IN BUSINESS 
 
 brief, but explicit titles. A title should be a concise 
 epitom6 of the contents of a table. It is not its pur- 
 pose to include all of the facts which a table contains. 
 It should be short, well punctuated, clearly phrased, 
 and incapable of being misconstrued. Titles are 
 generally faulty because of omissions and an inverted 
 order in the characteristics which are named. The 
 natural order is from superior to subordinate items. 
 
 Classification and tabulation generally require that 
 the facts be grouped, or condensed. It is impossible 
 to retain the individuality of each item. Abbrevia- 
 tion — a sort of telescoping — is necessary, but it is 
 also dangerous, because it sacrifices accuracy. Con- 
 ciseness and brevity are desirable in tables, but not at 
 too great a sacrifice. How far grouping may go 
 depends upon the problem in mind and the occasion 
 for classification. What it involves, however must 
 not be ignored. 
 
 Using the data in Table 3, the issues may be con- 
 densed as follows, but the detail which is necessary 
 for viewing the issues individually is lost. 
 
 Table 8. — Municipal Issues Classified by Net Interest Rate 
 
 Net interest rate, per cent. 
 
 Number of 
 issues 
 
 Amount of 
 issues 
 
 Total 
 
 16 
 
 $1,009,000 
 
 4.00 to 4.25.. 
 4. 25 to 4. 50.., 
 4.50 to 4.75.. 
 4.75 to 5.00.., 
 5.00 and over. 
 
 210,000 
 314,000 
 240,000 
 245,000 
 
CLASSIFYING AND TABULATING THE PACTS 49 
 
 More serious for detailed analysis is the grouping 
 shown in the following table. 
 
 Table 9. — Number of Income Tax Retubns by Classes, 1914-1916' 
 
 Inoomes 
 
 Total number of returns 
 
 
 1914 
 
 1915 
 
 1916 
 
 Total 
 
 357,515 
 
 336,652 
 
 429,401 
 
 
 
 $3,000- $4,000 
 
 82,754 
 
 66,525 
 
 127,448 
 
 34,141 
 
 15,790 
 
 8,672 
 
 5,483 
 
 6,008 
 
 3,185 
 
 5,161 
 
 1,189 
 
 406 
 
 233 
 
 130 
 
 147 
 
 69 
 
 114 
 
 60 
 
 69,045 
 
 58,949 
 
 120,402 
 
 34,102 
 
 16,475 
 
 9,707 
 
 6,196 
 
 7,005 
 
 4,100 
 
 6,847 
 
 1,793 
 
 724 
 
 386 
 
 216 
 
 254 
 
 122 
 
 209 
 
 120 
 
 85,122 
 
 4,000- 5,000 
 
 72,027 
 
 5,000- 10,000 
 
 150,551 
 
 10,000- 15,000 
 
 45,305 
 22,621 
 
 15,000- 20,000 
 
 20,000- 25,000 
 
 12,956 
 
 25,000- 30,000 
 
 8,055 
 10,068 
 
 30,000- 40,000 
 
 40,000- 50,000 
 
 5,611 
 
 50,000- 100,000 
 
 10,452 
 
 100,000- 150,000 
 
 2,900 
 
 150,000- 200,000 
 
 1,284 
 
 200,000- 250,000 
 
 726 
 
 250,000- 300,000 . . 
 
 427 
 
 300,000- 400,000 
 
 469 
 
 400,000- 500,000 
 
 245 
 
 500,000-1,000,000 
 
 376 
 
 1,000,000-and over 
 
 206 
 
 
 
 'American Economic Review, September, 1919, p. 503. 
 
 The distribution of the items within the groups is 
 concealed. Whether the items are concentrated at 
 the upper or the lower sides of the groups, or are 
 distributed uniformly through them, is not known. 
 
 The contents of tables should unmistakably bear 
 on the problems to which they relate. Extraneous 
 matter should be removed. Tables should be explicit 
 
50 STATISTICS IN BUSINESS 
 
 and contain a minimum of "unclassified," "not 
 stated," and "miscellaneous" material. If this type 
 predominates, it is either a suggestion of a desire to 
 withhold some of the detail, or evidence that the basis 
 of classification is faulty. 
 
 The scientific mind sees things in groups. It classifies 
 according to common characteristics, heterogeneous 
 and seemingly unrelated facts; traces out similarities, 
 and looks for cause and effect. It seeks underlying 
 principles through analysis. "Classification is indis- 
 pensable to, and accompanies every scientific infer- 
 ence," and tabulation involves far more than drawing 
 lines and inserting numerical symbols. It is a means 
 of recording classification and analysis. 
 
 But how is a business to study its problems by 
 means of tabulating the facts which it currently 
 receives? For most businesses it is unnecessary to 
 create an elaborate organization for this purpose. 
 Every business should provide some specialized 
 machinery to scrutinize currently the records which 
 are received, and to test by experiment the relation 
 which they have to current problems. This can be 
 done by tabulating the facts and by observing the 
 underlying principles which seem to determine them. 
 If the records do not contain all the facts which are 
 necessary either to explain a problem, or to furnish a 
 continuing picture of a business operation, it is neces- 
 sary to seek new data through additional records, or 
 through schedules sent to the various operating divi- 
 sions, or the groups concerned with operation, sales, 
 etc. If additional information on sales, on office 
 methods, on production costs, are required, this can 
 be secured by means of schedules, if they are properly 
 
CTiASSIFYING AND TABULATING THE FACTS 51 
 
 framed so as to enlist the support and cooperation of 
 those to whom they are sent. 
 
 The problems of classifying and grouping dissimilar 
 facts, of separating large aggregates into their several 
 parts, and of building up totals from details are 
 intimately related to the methods by which facts are 
 collected. Every step in the collection process in- 
 volves some sort of tabulation. Indeed, collection 
 and tabulation of facts are but two steps in one 
 general process of classification. 
 
 There is a technique in the method of collecting 
 facts which is important, and which business should 
 seek to apply. In every industry, departmental jeal- 
 ousies are common, sectional points of view maintain, 
 and it is frequently difficult to overcome them and 
 to secure the united cooperation of all in matters of 
 common interest. Personal interviews will help to 
 pave the way for securing information, and the tone 
 in which inquiries are made will serve to establish 
 confidence. Cooperation is indispensable, and any- 
 thing which will contribute toward it must be capital- 
 ized. Above all, suspicion must be allayed, and 
 sectional and narrow personal interests dispelled. 
 
 The preparation of schedules is simple, but funda- 
 mental principles should be observed. 
 
 First. — ^Assurance should be given, either within 
 the schedule itself or preparatory to its being sent, 
 that the inquiries are made for the good of the busi- 
 ness as a whole, and that it is mutually advantageous 
 that the questions be answered fully and accurately. 
 Cooperation must be solicited. The collection of 
 full and satisfactory information depends upon the 
 existence of good-will and mutual understanding. 
 
52 STATISTICS IN BUSINESS 
 
 Second. — Schedules, or inquiries, should be as brief 
 as is consistent with the purposes for which they are 
 intended, and the questions unmistakably addressed 
 to the problem involved. So far as is possible, the 
 relation of each question to the part of the inquiry 
 with which it is concerned, and to the problem as a 
 whole, should be evident. 
 
 Third. — The schedule form itself should be simple 
 and consistent with the type of records which exist, 
 so that supplying the information desired will not 
 involve an undue amount of labor and occasion error, 
 because of the necessity for reinterpreting the cus- 
 tomary units of measurement. 
 
 Fourth. — The questions should be simple, and 
 incapable of being misunderstood; and, so far as is 
 possible, answerable by "yes" or "no," or by number. 
 They should not allow of evasive answers, and should 
 not be unduly inquisitorial. The order in which 
 thfey are asked should be convenient for the person 
 addressed, and not involve unnecessary duplication, 
 or arouse a suspicion that the informant is to be in 
 any way tricked by his answer. 
 
 Information obtained directly from business records, 
 or from schedules based on records, should be sub- 
 jected to a thorough editing before the tabulation 
 process begins. Evident errors due to omissions, 
 additions, false interpretations, or misunderstandings, 
 should be corrected at once. Undue tampering with 
 the facts, however, is to be guarded against, and altera- 
 tions made only in case of unmistakable error. In 
 all cases, alterations should be made evident through 
 the use of some distinctive mark or ink device. It 
 is an easy matter materially to change the nature of 
 
CLASSIFYING AND TABULATING THE FACTS 53 
 
 a fact, and to distort the truth by the interchange of 
 a few items, or by entrusting the editing to an inex- 
 perienced person. So far as possible, the returns 
 should be made consistent with the facts, and complete. 
 This may necessitate the return of the schedule. If 
 it does, full explanation should be made of the reasons 
 for returning it, and cooperation solicited. 
 
 As soon as data are properly edited, tabulation 
 may at once proceed. This should be begun, how- 
 ever, only after a definite plan of classification has 
 been worked out, and the nature of the problem upon 
 which the classification is to throw light, clearly 
 sensed. All of the considerations noted above in this 
 respect are of primary significance. Indeed, in many 
 instances the nature of the tabulation wanted deter- 
 mines the type of the data which is collected. The 
 order of procedure in periodic studies, for instance, 
 where comparisons are currently made, is first to 
 decide upon the tabulations which are wanted, and 
 afterward to collect the data in such a way that the 
 purpose wiU be realized. In analyses of a trial charac- 
 ter, when the nature of the data is not known, the 
 form of tabulation must be largely experimental. The 
 form which it takes, even in such cases, simply serves 
 to put in tangible form a scheme of classification 
 already made. 
 
 The actual tabulating process may be done either 
 by machine or hand methods. Where the problem is 
 simple, and the data relatively few, hand tabulation 
 will sufiice. Where the problem is complex, and the 
 data numerous, some sort of machine tabulation must 
 be employed. There are on the market two standard 
 mechanical tabulating machines, the Hollerith and the 
 
54 STATISTICS IN BUSINESS 
 
 Powers, Either of them may be used to advantage 
 in large establishments where continuous and elabo- 
 rate use is made of statistical data. The process by 
 which tabulation by machine methods is carried on is 
 comparatively simple, and need not be described here. 
 In selecting statistical data from secondary sources 
 such as the Reports of the United States Census on 
 Manufactures or Occupations, or from such widely 
 used journals as Bradstreet's, care should be used to 
 see that the facts are comparable. Simply to take 
 prepared figures from different but complementary 
 sources, good in themselves, and to fit them into 
 tables, in order to substantiate a belief, or to see the 
 implication of your problems from a new angle, with- 
 out at the same time subjecting them to rigid tests 
 of accuracy, content, and application, is to confuse 
 the mechanics of tabulation, with logical analysis. 
 Tabular outUnes, neatly filled with figures which prove, 
 and with percentages which seem to show relations, 
 suggest so much care in preparation that they 
 often carry a conviction which is unwarranted. Their 
 neatness and form seem to guarantee the nature of 
 their contents. Tabulation is always a means, and 
 not an end, in statistical studies. The business con- 
 cern which consents consciously, or unconsciously, to 
 allow elaborate tabulations of facts currently to be 
 made, without continually subjecting them to tests 
 of validity, and application to particular problems 
 and issues, is not only wasting money but also violat- 
 ing the fundamental consideration which should con- 
 trol every business; namely, the scientific point of 
 view. 
 
CHAPTER V 
 PRESENTING THE FACTS— GRAPHICS 
 
 Classified facts may also be expressed graphically. 
 There is a psychology about graphic presentation 
 which is significant and which business can not afford 
 to ignore. Through tabulation, facts are only im- 
 perfectly visualized. Relations do not stand out; 
 they remain abstract. It is difficult to compare more 
 or less, to see differences, and to appraise the amounts. 
 Graphically, however, relations are seen; there is an 
 appeal to the eye, as well as to the intellect. A fact 
 is emphatic in proportion to the number of avenues 
 through which it makes its appeal. 
 
 But graphic presentation alone will not suffice. 
 Through classification and tabulation, facts are re- 
 duced to logical order; through graphic forms they 
 are illustrated according to this order. Graphic pre- 
 sentation aMs to the meaning of facts by throwing 
 it into relief. It does not replace tabulation; it com- 
 plements it. 
 
 In selecting diagrams or other graphic forms serv- 
 iceability, simplicity and truthful representation of 
 the facts should be the aim. There is always a best 
 form in graphics as there is in tabulation. The same 
 requirements as to order of arrangement of details, 
 spacing, size of the figure, and methods of making 
 the relations between facts emphatic, apply here as 
 they do in tabulation. The physical work of charting 
 
 55 
 
56 STATISTICS IN BUSINESS 
 
 may be assigned to the relatively inexperienced; the 
 choice of the forms to use must be made by one who 
 not only understands precisely what is to be shown, 
 the psychology of the persons to whom it is addressed, 
 but also appreciates the peculiar appeal of the differ- 
 ent illustrations that are available. 
 
 In choosing graphic figures certain elementary but 
 at the same time fundamental principles should be 
 followed. 
 
 First.— Avoid figures which must be read in two or 
 more dimensions. 
 
 Second. — Guard against confusing the apparent 
 with the real. In this connection, lines or bars are 
 superior to surfaces and solids. 
 
 Third. — Accompany graphic forms with the con- 
 crete data which they represent. 
 
 Fourth. — -See that the fact and the form of its pres- 
 entation agree. 
 
 Where areas are involved, choose some form of 
 statistical map as a means of illustration. Maps 
 show both position and magnitude. Data may be 
 spread out on them and studied in relation to space. 
 Strive for that degree of accuracy in map making 
 which your problems require, and remember that 
 maps, like all types of diagrams, are serviceable, 
 primarily, in the power of suggestion, rather than in 
 their truthful portrayal of precise facts. (See Figs. 
 21, 22, 23 and 24.) Suit the graphic device to the 
 problem to be solved. Use the same discrimination 
 here that you use in the preparation of the data for 
 illustration; choose the means in conformity with the 
 ends. 
 
 Some forms of data may be shown to advantage in 
 
PRESENTING THE FACTS 57 
 
 graphs or curves. When a continuous picture is 
 desired, either as a means of describing a variable fact 
 at one time, or a constant fact over a period of time, 
 a graph or curve has distinct advantages over a column 
 of figures. If, for instance, wage-rates or earnings are 
 to be studied, reduce them to graphic form. Choose 
 scales which will throw them into reUef, but which will 
 neither exaggerate the exceptionally large, nor lose 
 sight of the exceptionally small units. Study the 
 direction and shape of the distribution and try to see 
 the facts in relation to each other, and to the whole. 
 
 Along the horizontal scale, plot the measurements, 
 and on the vertical scale list the frequency with which 
 each measurement occurs. Make the steps on both 
 scales equal units (see Figs. 4 and 20). Under no 
 circumstances should there be doubt as to the meaning 
 of the units or the spaces by which they are repre- 
 sented. Let the illustration be a faithful representa- 
 tion of the fact. Do not attempt to give an arbitrary 
 direction to the curve, nor smooth it unless the imper- 
 fections of the data suggest it, or the character of the 
 samples makes it necessary. The classification which 
 precedes the graphic presentation is the means of 
 analyzing it; the graphic figure chosen is the device 
 for illustrating it. 
 
 When the facts which are studied are historical, 
 i.e., extend over a period of time, an historical curve 
 may be used to illustrate them. Scientific method in 
 the classification must remove the uncertainties of 
 such an analysis. Periods which have nothing in 
 common, and units of measurements which have 
 changed dm-ing the periods, cannot be compared. 
 An historical curve will rarely, if ever, reveal incon- 
 
58 STATISTICS IN BUSINESS 
 
 sistencies. All that can be expected of it, is faith- 
 fully to record the changes from time to time. If 
 these are fictitious, the curve is not to blame; the 
 error is in subjecting them to this treatment. The 
 analysis is fundamental; the curve only suggestive. 
 
 Business executives cannot afiford to ignore the 
 merits of graphic presentation, but they must not be 
 deluded into the belief that it carries with it a magic 
 which makes it unnecessary to look behind it. Reason- 
 ing from graphic figures alone, where the conditions of 
 the measurements which they represent are not known, 
 violates every canon of scientific method. The super- 
 ficial is confused with the fundamental. 
 
 Business problems and business facts must be taken 
 apart and scrutinized. Classification is the first step 
 in this process, and graphic presentation the means by 
 which the classification is expressed. No business is 
 too small to profit by this approach, and none is too 
 large to ignore its possibilities. The requirements of 
 scientific method furnish the conditions under which 
 analysis is applied. 
 
 It is impossible in a brief statement adequately to 
 discuss the technique of graphic presentation. For 
 a more complete discussion reference should be made 
 to the author's "Introduction to Statistical Methods," 
 and to Brinton, W. C, Graphic Methods for Pre- 
 senting Facts. It may be helpful, however, partly in 
 emphasis of what has been said, and partly for the 
 sake of convenience, to summarize in the form of 
 general rules, the salient points to be remembered in 
 the use of graphic figures.^ 
 
 1" Rules for Graphic Presentation of Statistical Data," by Day, 
 Reed and Secrist. Weekly Statistical News, Central Division of 
 Planning and Statistics, Washington, D. C, No. 5, Oct. 10, 1918. 
 
PRESENTING THE FACTS 59 
 
 A. General Make-tjp of Diagrams 
 
 1. Data to Accompany Diagrams. — The data shown 
 graphically in a diagram should be given in tabular 
 form either beside or within the diagram, or in close 
 proximity in the text. Care should be exercised, 
 however, to place figures so as not to disturb or distort 
 the visual impression conveyed by the chart. (See 
 Fig. 1 where this rule is followed, and Figs. 2 
 and 3, where it is violated. In Fig. 1, for instance, 
 the inclusion of the concrete data makes it possible 
 to verify the percentages upon which the diagram 
 is drawn. In Fig. 2, this is impossible.) 
 
 2. Scale Units. — In general, in the laying off of 
 scales, the scale intervals on any single diagram should 
 be exactly proportionate to the gradation of number, 
 size, or time represented (the logarithmic scale con- 
 stitutes an exception to this rule). (See Fig. 4, 
 where this rule is seriously violated. The scale units 
 on the horizontal axis are not proportional to the sizes 
 of the groups into which the capital data are divided. 
 Had the rule been followed, the direction of the curves 
 would have been distinctly less vertical and the visual 
 impression different. See also Fig. 20 where the 
 rule is violated on the horizontal axis. If the space 
 units were proportional to the amounts, the curves 
 would be drawn out much farther to the right.) 
 
 3. Scale Figures. — Figures for the scales of diagrams 
 should be placed at the left and at the bottom, or 
 along the respective axes. 
 
 4. Base Lines.— It is well to distinguish — ^as by 
 heavier inking — Unes which represent standards of 
 attainment or bases of measurement or comparison. 
 
60 STATISTICS IN BUSINESS 
 
 (See Figs. 5 and 6. In the first, the rule is violated; 
 in the second, it is followed. In Fig. 6, the base 
 line for both series is presumably 100, and constitutes 
 — ^although this is not stated on the diagram — the 
 average for the year, the monthly prices being com- 
 puted and plotted as differences, more or less from this 
 amount. In Fig. 5, both prices and quantities 
 are measured from zero, and the line represent- 
 ing it should have been inked heavier than the other 
 lines.) 
 
 5. Arrangement of Items. — Items should be grouped 
 so as to facilitate the comparison of those most sig- 
 nificantly related. Within groups, some systematic 
 order should be adopted. The most serviceable 
 arrangements are according to (a) the sequence of 
 the items in time, with the earliest at the left; (6) the 
 size of the items, with the largest at the top or at the 
 left; or (c) the favorableness of the items, "with the 
 most favorable at the top or at the left. (See Figs. 
 7, 8, and 9. In Fig. 7, the amount controls the 
 order of the states, the largest amount coming first. 
 In Fig. 8, the order of the states is determined by 
 the geographical position which they have in passage 
 across the country from East to West. In Fig. 9, 
 the order from top to bottom seems to be haphazard. 
 Frequency would have suggested itself as the natural 
 order.) 
 
 6. Position of Titles. — So far as practical, all print- 
 ing upon a diagram should be placed so as to be 
 read with ease from the bottom of the sheet. (This 
 is pretty much a matter of preference. In the origi- 
 nals of the following figures the practice was about 
 
PRESENTING THE FACTS 61 
 
 equally divided. So far as the writer is concerned, 
 the position of the title is not a relatively important 
 matter.) 
 
 7. Use of Colors. — Where a need for duplicates 
 may arise, charts should be made entirely in black 
 and white. The use of colors is not recommended 
 except for large wall charts. 
 
 8. Size of Sheet. — Avoid irregular sizes of paper. 
 As far as practical, the established correspondence 
 sizes (8 X 103^ or 8^^ X 11) should be used. 
 
 B. Choice of Graphic Forms 
 
 1. For Simple Comparisons of Size. — (See Figs. 
 10 and 11, where surfaces and bars are used as alterna- 
 tives for illustrating size. In all of the figures, bars 
 or single dimension illustrations are clearly preferable. 
 Avoid such an illustration as Fig. 12. In Fig. 13, 
 the illustrations are suggestive but confusing since 
 the scale is not given and two dimensions are 
 used.) 
 
 (a) Bars. — Bars are the most satisfactory graphic 
 device for this purpose. In general, all the bars used 
 in the diagram of a single study should be of uniform 
 width. 
 
 (6) Lines. — When a large number of separate items 
 have to be shown in a single diagram, lines may be 
 employed in place of bars. 
 
 (c) Position. — Bars (or lines) are best placed hori- 
 zontally. 
 
 2. For Comparisons of Component Parts. — (See 
 Figs. 14, 15, and 16. In Fig. 14, cross-hatched 
 
62 STATISTICS IN BUSINESS 
 
 columns are placed vertically, and in Figs. 15 and 
 16, horizontally. The vertical columns are more 
 readily compared than are those which are horizontal. 
 In Fig. 15, the more recent year is placed at the 
 bottom, while in Fig. 16, the order of the years is 
 reversed. These figiires should be contrasted, with 
 the pie-diagrams shown in Figs. 1, 2, and 3, as 
 means of illustrating component parts.) 
 
 (o) Subdivided Bars. — Subdivided bars are the 
 most satisfactory form for this case. 
 
 (6) Cross-hatching. — Cross-hatching is the best way 
 in which to distinguish component parts. 
 
 (c) Posifo'on. —Horizontal bars are to be preferred 
 to vertical, except when the items are separated by 
 intervals of time, in which case vertical bars should 
 be used. 
 
 3. For Displaying Frequency Distributions. 
 
 (a) Vertical Column. — In general, the vertical bar 
 (or column) form is to be used. The straight-line 
 histogram, however, is a satisfactory alternative. 
 (See Fig. 20, where the histogram is used.) 
 
 (6) Position of Scales. — The scale for the variable 
 is to be placed along the horizontal axis; the scale for 
 the frequencies along the vertical axis. 
 
 4. For Showing Geographic Variations. 
 
 (a) Dot Maps. — Where the variable takes the form 
 of varying numbers of a given item, the situation is 
 best represented by a dot map, in which each dot 
 represents a fixed number of cases. All of the dots 
 should bo of uniform size. (Figs. 21, 22, 23, and 
 24, show four types of dot maps. Fig. 21 gives 
 only an impressionistic view of frequency, but is well 
 
PRESENTING THE FACTS 63 
 
 fitted for this purpose. Places of "high" and "low" 
 density are brought out in a remarkable manner. 
 Fig. 22 fails of its purpose, because the size of the 
 dots cannot be readily compared. The exact amount 
 could be better illustrated by a cross-hatched surface 
 as in Fig. 24. Fig. 23, likewise, illustrates an unsatis- 
 factory map device for much the same reasons as 
 those noted concerning Fig. 22.) 
 
 (6) Shaded Maps. — Where a continuous variable 
 is to be shown, solid black and white, and graded 
 cross-hatched areas constitute the most satisfactory 
 form. Care should be exercised to secure gradations 
 of intensity of black and white corresponding closely 
 to the gradations of the variable. 
 
 5. For Showing Time Variations. 
 
 (a) Straight-line Graph. — In general, the use of the 
 straight-Une graph between plotted points, is to 
 be recommended. (Fig. 25 shows typical straight- 
 line historical graphs. In this case, two vertical 
 scales are employed, and care must be used in inter- 
 preting the hues. In Figs. 18 and 26, vertical bars, 
 and in Fig. 19, horizontal bars, rather than con- 
 nected lines, are used to show data historically. 
 Where the increase or decrease over a period is con- 
 tinuous and uninterrupted, this form of illustration is 
 satisfactory. Where the tendency is irregular, con- 
 tinuous lines should be used. Care, however, should 
 be employed, so as not to assign meaning to the direc- 
 tion of the lines connecting the points when they are un- 
 related, and to confuse absolute with relative changes. 
 In this connection, see Fig. 27 and the discussion 
 relating to it.) 
 
64 STATISTICS IN BUSINESS 
 
 (b) Position of Scales. — Intervals of time should be 
 scaled invariably along the horizontal axis. (See 
 Figs. 13 and 19, where this rule is violated.) 
 
 (c) Zero of Vertical Scale. — There is a strong pre- 
 sumption in favor of the appearance of the zero on the 
 vertical scale on the chart. (On the logarithmic or 
 "ratio" chart there is no zero line.) 
 
 (d) Logarithmic Scale. — The vertical logarithmic 
 scale is to be used when rates of change or propor- 
 tionate increases and decreases are to be emphasized. 
 When the logarithmic scale is employed, the limits of 
 the scale should be at some power of ten. (See 
 Figs. 28 and 29, and the discussion accompanying 
 them.) 
 
 These rules are general, and should, so far as is 
 possible, be applied to all graphic forms. Each busi- 
 ness, however, must meet its problems in the light of 
 their peculiarities, and adjust the graphic illustra- 
 tions to the most appropriate ends. The making of 
 diagrams and curves is never an end. Diagrams 
 should be considered as a means of throwing light on 
 current and basic problems, and should constantly be 
 adjusted to the individual for whom they are prepared, 
 and the problems which they illustrate. A diagram 
 designed to furnish an executive with a concise 
 picture of an operation, or a series of operations, will, 
 of course, be different from one which is designed for 
 the public at large. Graphic forms are significant 
 primarily because of what they suggest, and the psy- 
 chology and intelligence of the group for which they 
 are prepared should constantly. be kept in mind. 
 
PRESENTING THE FACTS 
 
 65 
 
 Graphic presentation is an art, and too much atten- 
 tion cannot be given to it on the part of the modern 
 executive who desires to apply to his business the 
 scientific point of view. 
 
 Fig. 1. — Pie-diagram showing the distribution of total stock of 
 hams, bacon and shoulders, reported August 31, 1917. 
 
 Wholesale Dealers 2.8 
 
 Setatl Dealers 3.39 
 
 MlBcellaneoaa 
 3.9% 
 
 Stock Reported (Pounds). 
 
 Meat packers 361,932,276 
 
 Storage warehouses 25,512,057 
 
 Wholesale dealers 11,940,169 
 
 Retail dealers 14,368,359 
 
 Miscellaneous 16,654,367 
 
 Total 430,407,228 
 
 The above figure and those following illustrate dif- 
 ferent forms of graphic presentation. Some of them 
 follow and some violate the rules given above — with 
 what consequence, the reader must in large part 
 determine for himself. Some of the more outstanding 
 
66 
 
 STATISTICS IN BUSINESS 
 
 virtues and limitations of the figures are given in the 
 comments which accompany them. 
 
 In Fig. 1, the surface of the circle constitutes 
 100 per cent, or the entire amount of stocks reported, 
 as shown in the table below the figure. An alternative 
 and generally more satisfactory way of showing com- 
 ponent parts is by using bars the lengths of which are 
 
 Fig. 2. — Pie-diagram showing the percentage distribution of 
 the world's mill supply of cotton contributed by each country; 
 1917. 
 
 proportionate to the amounts (see Figs. 14, 15, 
 and 16.) The table beneath the illustration would 
 have been more complete had it contained the per- 
 centage figures illustrated in the diagram. 
 
 Fig. 2 is faulty in not containing the concrete 
 data on the basis of which the percentages are 
 computed. Moreover, the relations between the per- 
 
PRESENTING THE FACTS 
 
 67 
 
 centages are not as clearly illustrated as they would 
 have been had bar-diagrams been used. (See Figs. 
 14, 15, and 16.) 
 
 The pie-diagrams below are presumably drawn in 
 proportion to the amount of the goods produced, but 
 there is nothing in the illustrations to show this, nor 
 
 Fig. 3. — Pie-diagrams showing the percentage distribution of the 
 production of boots and shoes, and of textiles, by states. 
 
 1 MASSACHUSETTS 
 
 2 HEWYORH 
 
 3 MISSOURI 
 
 4 NEW HAMPSHIRE 
 9 OHIO 
 
 e PENNSTLVANIA 
 T ILLINOIS 
 
 COTTON 600DS. 
 rNCLJUDINQ COTTON 
 SMALL WARES 
 
 BOOTS 
 
 8. MAINE 
 
 9 WISCONSIN 
 
 10 NEWJERSElf 
 
 11 MINNESOTA 
 
 12 VIRGINIA 
 
 13 MICHIQAN 
 
 14 AaoniER STATE 
 
 WOOtfN a WORSTED 
 
 600DS. INCLUDIN6 
 
 FELT GOODS a 
 
 WOOL HATS 
 
 I MASSACHUSETTS 
 2 mm CAROUNA a new Hampshire 
 
 3 SOUTH CAROJNA 
 
 4 RHODC ISLAND 
 
 e asKeiA 
 e PonemfflNiA 
 T coNNEcncur 
 
 8 ALABWU 
 
 10 MAINE 
 
 11 NEW YORK 
 
 12 NEW JERSEV 
 
 13. AaOniQl STATES 
 
 2 PEMEVUMW 
 
 3 RKODE ISLAND 
 
 4 NEW JERSEY 
 9 NEW YORK 
 
 e oonccncuT. 
 
 MASSACHUSETTS 
 
 7 MAINE 
 
 8 NEW HAUPSHRe 
 
 9 OHIO 
 
 o warn 
 
 II AaOTHERSIXIES 
 
 is the scale given in which the measurements are made. 
 Moreover, the concrete data are missing — both the 
 amounts and the relationships have to be taken on 
 faith. The use of bar-diagrams would have been 
 preferable here, as in Figs. 1 and 2. 
 
 Fig. 4 is reproduced exactly as it appears in the 
 
68 
 
 STATISTICS IN BUSINESS 
 
 original. It is defective in several respects. The 
 vertical scale contains the unit 9000 instead of 900. 
 The horizontal scale is divided into uniform spaces, 
 but these are related to varying amounts. The in- 
 
 FiG. 4. — Curves showing the relation of farm capital to labor in- 
 come on 260 general farms in Monmouth County, New Jersey. 
 
 Labor Income 
 $1300 
 
 1200 
 1100 
 1000 
 
 9000 
 
 800 
 
 700. 
 
 eoo 
 soo 
 
 400 
 300 
 200 
 
 >£oii 100 
 200 
 
 
 
 
 
 / 
 
 --—-^ 
 
 
 
 
 
 / 
 
 
 
 
 
 
 / 
 
 
 
 
 
 '^\ 
 
 / 
 
 ^ 
 
 
 
 
 i/ 
 
 .y 
 
 ^v 
 
 
 
 - 
 
 f A 
 
 
 
 
 
 / 
 
 Yof^ 
 
 
 
 
 
 // 
 
 / 
 
 
 
 / 
 
 \^ 
 
 // 
 
 
 
 
 / 
 
 \ 
 
 '/ 
 
 
 
 
 /J 
 
 
 
 
 
 
 f 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 f 
 
 
 
 
 
 
 $3000 
 
 $5001 
 
 $7001 
 
 $10001 
 
 $15001 
 
 $20001 
 
 $30001 
 
 to 
 
 to 
 
 to 
 
 to 
 
 to 
 
 to 
 
 and 
 
 :ooo 
 
 7000 
 
 10000 
 
 15000 
 
 200OO 
 
 3O0O0 
 
 over 
 
 Total Capital Invested per Farm 
 
 terval, presumably, is $2000 between $3000 and $7000 
 (but, see the different ways of recording the lower sides 
 of the first two groups). The intervals above $7000 
 are in order, $3000, $5000, $5000, $10,000, and an 
 indefinite amount, but the scale is drawn as though 
 
PRESENTING THE FACTS 
 
 69 
 
 they were identical. The result of this error is to 
 give a false direction to the curves. 
 
 The base or zero line in Fig. 5, should have been 
 more heavily inked than the other lines. The spaces 
 assigned to the months represent in fact a series of 
 rectangles the heights of which are indicated by the 
 positions of the curves at the middle points. The 
 lines connecting the points on the production curve 
 
 Fig. 5. — Graphs showing the price and production of eggs by 
 months on selected farms, Washington Co., Ohio, 1912-1916. 
 
 •f nnn 
 
 
 
 
 
 
 
 
 
 
 
 
 
 40 
 
 a 
 
 30 » 
 
 S 
 
 20Q 
 
 1 
 g 
 
 10 -c 
 
 
 Egg Production • Dozens 
 
 ,/^ 
 
 e'^c, 
 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 N 
 
 
 
 ?A 
 
 
 
 
 
 
 / 
 
 
 
 
 \ 
 
 h 
 
 / 
 
 \ 
 
 
 
 
 / 
 
 y 
 
 
 
 
 \ 
 
 v/ 
 
 
 \ 
 
 
 
 / 
 
 / 
 
 
 
 
 
 
 ^ 
 
 s.^ 
 
 y^' 
 
 ^^ 
 
 .-- 
 
 ^ 
 
 
 
 
 
 
 y 
 
 
 
 
 
 \ 
 
 s_ 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 s 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 Not 
 
 Dec 
 
 JaD, 
 
 Feb. 
 
 Mar 
 
 Apr 
 
 M»y 
 
 June 
 
 July 
 
 Aug 
 
 Sep 
 
 Oct. 
 
 have no other purpose than to aid the eye in interpret- 
 ing the increase or decrease from month to month, 
 and in noting the general contour of the curve. The 
 points on the price curve for the months presumably 
 represent averages so that no significance should be 
 attached to the lines connecting these points. It is 
 not clear from the curves why the beginning and stop- 
 ping points are not the middle of the month spaces. 
 The curves clearly show the inverse relationship be- 
 tween production and price. 
 
 The base or 100 per cent, line in Fig. 6 is rightly 
 
70 
 
 STATISTICS IN BUSINESS 
 
 more heavily inked than the other lines so that supply 
 and price in excess and in defect of it are clearly shown. 
 
 Fig. 6. — Curves showing by months the relative supply and 
 price of Wisconsin butter, 1914. 
 
 200 
 190 
 180 
 
 
 
 SUPPLY AND PRICES OF WISCONSIN 
 
 
 
 2U0 
 190 
 
 
 
 BUTTER- 1914 
 Supply Index .0^ -0 — 0- — 
 
 
 
 
 
 Price Index 
 
 
 
 
 
 170 
 160 
 150 
 HO 
 
 
 170 
 150 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 150 
 140 
 130 
 120 
 
 
 
 
 
 1 
 1 
 1 
 
 1 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 1 
 1 
 1 
 1 
 
 
 \ 
 \ 
 
 
 
 
 
 & 120 
 
 
 
 
 
 / 
 
 
 \ 
 
 
 
 
 
 
 
 1 
 1 
 1 
 
 
 
 
 \ 
 
 \ 
 
 \ 
 
 3 
 
 ^ 
 
 
 110. 
 
 
 
 100 
 
 \ 
 
 
 
 1 
 t 
 1 
 
 1 
 
 
 
 
 ^ 
 
 
 / 
 
 3 
 
 
 100 
 
 90 
 
 
 N 
 
 k 
 
 1 
 1 
 
 1 
 1 
 
 
 _-- 
 
 y 
 
 
 
 \ 
 
 \ 
 \ 
 
 
 
 
 
 / 
 
 / 
 
 l^ 
 
 
 
 
 
 
 1 
 
 \ 
 
 80 
 
 1 
 
 70 
 
 60 
 SO 
 
 
 / 
 
 / 
 1 
 
 
 
 
 
 
 
 
 \ 
 \ 
 
 --^ 
 
 
 
 
 
 
 
 
 
 
 
 70 
 60 
 
 
 
 
 
 
 
 
 
 
 
 
 50 
 
 Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Hov. Dec. 
 
 It will be noticed that the 100 per cent, line bisects the 
 areas inclosed within both curves — that is, the excesses 
 
PRESENTING THE FACTS 71 
 
 are equal to the deficiencies. In this figure, the months 
 or horizontal units are indicated by a line rather 
 than by a space as in Fig. 5. There are eleven 
 spaces in this figure; in Fig. 5, there are twelve 
 spaces for the year. There is no question in this 
 figure about the points at which these curves should 
 begin and end as there is in the preceding one. 
 
 From the curves it may be deduced that the supply 
 and the price are relative, rather than absolute num- 
 bers, but the value of the illustration would have 
 been increased had this fact been stated in some such 
 form as follows: 
 
 Average monthly price for the year = 100 per cent. 
 
 Average monthly supply for the year = 100 per 
 cent. Moreover, the concrete data should have been 
 included in the chart. The figure clearly shows that 
 the price of butter is much more stable than is the 
 supply. 
 
 The bar-diagram, (Fig. 7), illustrates the stocks of 
 sugar held by retail dealers by states in the order of 
 amounts. The largest is put first and is therefore 
 given emphasis, but the reverse order would have been 
 equally good. An alphabetical arrangement of the 
 states would have been meaningless for the purpose of 
 the illustration. The bars are placed horizontally and 
 are disconnected. Because of the regularity of the 
 decline from the greatest to the smallest amount, 
 little advantage would have accrued from connecting 
 the ends of the bars by straight lines. The diagram 
 suggests the relative amounts and that is all that it is 
 intended to do. The concrete data are made a part 
 of the diagram, and there is no occasion in studying 
 
72 
 
 STATISTICS m BUSINESS 
 
 Fia. 7. — Bar-diagram 
 dealers, 
 
 showing stocks of sugar reported by retail 
 by states, August 31, 1917. 
 
 K.I. 
 
 Pa. 
 
 111. 
 
 Ohio 
 
 Texas 
 
 Mass. 
 
 Oaltf. 
 
 Uleh. 
 
 lewa 
 
 Ind. 
 
 Wash. 
 
 Ho. 
 
 Wis. 
 
 La. 
 
 K.J. 
 
 Mebr. 
 
 Ore. 
 
 Kr. 
 
 Minn. 
 
 Okla 
 
 Md. 
 
 Ta. 
 
 Oolo 
 
 Tenn. 
 
 Can. 
 
 W.Va 
 
 Mont. 
 
 Oa. 
 
 Oenn. 
 
 K.O. 
 
 S.O. 
 
 Idaho 
 
 Ala. 
 
 S.D. 
 
 Ark. 
 
 K.D. 
 
 N.M. 
 
 Miss. 
 
 Me. 
 
 Ariz. 
 
 Fla. 
 
 D.O. 
 
 Wyo. 
 
 N.H. 
 
 B.I. 
 
 Utah 
 
 Vt. 
 
 Not. 
 
 Del. 
 
 Millions of Pounds 
 4 6 
 
 
 ^^■■" 
 
 
 
 ■■■■■ 
 
 
 ^^^^^^ 
 
 
 
 ^^^^^* 
 
 
 ^^^^^J 
 
 
 ^^^^^^ 
 
 
 
 ^^^^™ 
 
 
 ^^^* 
 
 
 ^^^^^J 
 
 ^^^^^^ 
 
 
 
 I^^^JJ 
 
 ^^J 
 
 
 ^^^^^* 
 
 ^^^ 
 
 
 ^^^^^J 
 
 ^ 
 
 
 ^^^^2 
 
 
 
 ^^^^^~ 
 
 
 ^^^^^^^ 
 
 
 ■^^^H 
 
 
 ^■■^ 
 
 
 
 ■I^H 
 
 
 ■^^H 
 
 
 ■■ 
 
 
 ■■ 
 
 
 ■■ 
 
 
 iB 
 
 
 ■ 
 
 
 ■ 
 
 
 ■ 
 
 
 I 
 
 
 
 
 I 
 
 
 1 
 
 llllllllllllllllllllli. 
 
 
 
 STOCKS REPORTED (Pounds) 
 
 N.T. 10.172.026 W.Va. 2.090.675 
 Pa. 10.010.887 Mont. 2.083.541 
 111. 8.433.880 Ga. 2.007,991 
 Ohio 7,330,061 Conn. 1.827.506 
 Texas 6,157.632 N.O- 1.815,797 
 Mass. 6,103.538 S.O. 1.662,631 
 Oallf. 6.069,864 Idaho 1,646,350 
 Mich. 4,538.117 Ala. 1.601,577 
 Iowa 4,314,304 S.D. 1,411,225 
 Ind. 3,940,366 Axk. 1.319,930 
 Wash. 3.151.117 N.D. I.e95,365 
 Mo. 3.6S3.S67 N M. 1,061.774 
 Wis. 3,436,810 Miss. 958.218 
 La. 3.183,312 He. 931,708 
 N.J. 3.161.345 Arls. 802.156 
 Nebr. 3,047,937 Fla. 798,624 
 Ore. 2,883.619 D.O. 783,297 
 Ky. 2,682,282 Wjo. 780,059 
 Minn. 2,659.989 N.H. 764.S02 
 Okla. 2,485.711 R.I. 724,(08 
 Md. 2,343,912 Utah 612,033 
 Va. 2,326,338 Vt. 667,096 
 Colo. 2,230,573 NeT. 605 J02 
 Tenn. 2,197,609 Del. 86,262 
 Kan. 2,189.351 
 
 
 1 1 1 
 
PRESENTING THE FACTS 
 
 73 
 
 Fig. 8. — Bar-diagram showing, by states, and for farm mortgages 
 the percentage of business on which commission is paid. 
 
 I lKSTUU4CNf COdKISSlOn 
 
 I novMCe CoHHISSlON 
 
 I No COHHISSICM. 
 
 STATE 
 
 PER CENT.OFTOTnL fflRM MORTCflCE BUSINESS 
 
 Mt. 
 
 KM. 
 
 Vr. 
 
 Miss. 
 
 Rl 
 
 Conn. 
 
 KY. 
 
 N.J. 
 
 Pa. 
 
 Ohio 
 
 Ino. 
 
 III. 
 
 Mich. 
 
 Vis. 
 
 Minn. 
 
 Iowa 
 
 Mo 
 
 M.D. 
 
 S.D. 
 
 NCBR. 
 
 Kans. 
 
 Del. 
 
 Mm 
 
 Va. 
 
 WVa 
 
 NC. 
 
 S.C 
 
 Ca. 
 
 Pla. 
 
 «Y. 
 
 Tenn. 
 
 Ala 
 
 Miss. 
 
 Ara. 
 
 La. 
 
 OlUA.. 
 
 Ttx. 
 
 Mont 
 
 Idaho 
 
 Wto, 
 
 Colo. 
 
 N.M. 
 
 l\mz. 
 
 Utah 
 
 Vash. 
 
 Out. 
 
 CALir. 
 
 jummi mmm 'Mmm, 'mnymi. ;^;^^^ w/M;m. T^pamm. wmtm. mwm. wmm 
 
 i^ 
 
 mm>>y. Trnm^^ mmm mmm 
 
 wmmL^^m 
 
 ^^ 
 
 U '/////////////. ^/A-mx^fu; v//////m/, -/////v/m/, 7//////y/M. WHJmHi 
 
 ma^^^m. 
 
 maKM^^^ 
 
 ^m&'^^^^^m. 
 
 wtm^^^sm^ 
 
 ^^ 
 
 ^IH^SSS^ 
 
 ■■il^^^^^^ 
 
 ■■■^^^^^^ 
 
 ^^^^'l^^WiMii.'MiiMi^^Mi'iimMiiii^li.iiiii^ 
 
 '/^.■>^y////yW 
 
 wmm^m^^i^ 
 
 w/MMy. 
 
 yyyyyyamx!- •mi:^^, yyy.ljMyyy/, 
 
 ■^1^^^^^ 
 
 ■H^^^^ 
 
74 STATISTICS IN BUSINESS 
 
 the illustration to determine the exact amounts for 
 the individual states. 
 
 The bar-diagram, (Fig. 8), illustrates for each of the 
 states the percentage distribution of commissions on 
 farm mortgages. The order of the states is geograph- 
 ical and the illustration not convincing because of this 
 fact. If the size of "Installment commission," for 
 
 Fig. 9. — Bar-diagram showing the per cent, distribution of 
 reasons for workmen leaving their positions. 
 
 WHY MEN LEFT 
 REASONS FOR LEAVING 
 
 REASONS . PERCENT 
 
 WOT ENOUGH MOHEY 9 P^^lj^ ^^ -^ 
 NEVER STARTED 6 ["....viL.;..! 
 
 VTORKING CONDITIONS 20' 
 
 lEZ5I3 
 
 DISCHARSED 
 
 t^lO OFF I g^ 
 
 DISSATISOED . z W ^ 
 
 BETTER OOB 13 PS'.'.- ..' -.liliSi;^ 
 
 — r 5 1 
 
 NEEDED AT HOME 8 !... .____i^ 
 LIVING CONDITIONS si. 
 
 
 FAILED TO REPORTae E 
 PERSONAL REASOHS 7 
 
 instance, had been made the controlling factor, the 
 dominant element in the illustration, as indicated 
 by the shades, would have been made emphatic. 
 There is always a best order to follow, and it should 
 govern in the make-up of a diagram. 
 
 This figure shows relative rather than absolute 
 amounts, and should have been accompanied by the 
 concrete data on which the percentages are computed. 
 
PRESENTING THE FACTS 
 
 75 
 
 The bar-diagram, (Fig. 9), is defective in the follow- 
 ing particulars: (1) It is not provided with a scale. 
 (2) The order in which the reasons are given is with- 
 out significance: it is not emphatic. (3) The concrete 
 
 Fig. 10. — Surfaces and bar-diagrams showing for specified years, 
 the amount of wheat in bushels purchaseable for $100.00. 
 
 A HUNDRED DOLLARS' WORTH OF WHEAT 
 
 1913 
 
 1914 
 
 1915 
 
 1916 
 
 data upon which the percentages are calculated are 
 not given. 
 
 In Fig. 10 surfaces and bars are used as alter- 
 native illustrations. The "sacks" vary both in 
 length and width, and the question is raised immedi- 
 
76 
 
 STATISTICS IN BUSINESS 
 
 ately: Are they drawn to scale? They are not so 
 drawn. The amounts and the illustrations may be 
 contrasted as follows, if 1913 is taken as 100. 
 Amounts: 1913 = 100; 1914 = 83; 1915 = 81; 1916 
 = 54. 
 
 Fig. 11. — Surfaces and bar-diagrams showing the relationship be- 
 tween the areas of Russia in Europe and the Russian Empire. 
 
 2,500 5,000 7,500 
 
 Square Miles Oa'COO) 
 
 Illustrations: 1913 = 100; 1914 = 67; 1915 = 54; 
 1916 = 30. 
 
 If the "sacks" are thought of as solids, then the 
 discrepancy between the fact and the illustration 
 is much greater. The drawings were presumably 
 made with the length only in mind, but they are 
 deceptive because both the length and the width vary. 
 For surfaces, the dimensions vary as the square roots 
 
PRESENTING THE FACTS 
 
 11 
 
 of the areas; and for solids, as the cube roots of the 
 contents. 
 
 The amounts are accurately and better illustrated 
 by the bars. There is nothing deceptive about them; 
 
 Fig. 12. — Surfaces showing the relationship between total coal 
 production and savings in coal consumption resulting from cur- 
 tailing light. 
 
 their accuracy is at once confirmed by the scale accord- 
 ing to which they are drawn. 
 
 In Fig. 11, surfaces and bars are used as alter- 
 native illustrations. Contrast the effect. Which 
 method seems to you preferable as an illustration? 
 
 In Fig. 12, surfaces or areas within areas are 
 used. Because, in such figures, the dimensions vary 
 
78 
 
 STATISTICS IN BUSINESS 
 
 as the square roots of the areas, comparison is very 
 difficult, if not impossible to visualize. Such illustra- 
 tions ought not to be used. 
 
 Fig. 13.— Surfaces and bar-diagrams showing gross tonnage 
 of vessels registered in Canada and Great Britain, engaged on 
 the Great Lakes and connecting waters west of Montreal. 
 
 4 iLj 
 
 1899-1900 
 
 FiuilTMr 
 
 Ho. si 
 VmmIi 
 
 arou 
 
 Touuffa 
 
 1B9B-1W0 
 
 insuu 
 
 »t 
 
 no 
 m 
 
 ao.Ki 
 
 167,026 
 
 sia,i;e 
 
 1905-1906 
 
 1913-1914 
 
 1899-1900 
 
 1905-1906 
 
 1913-1914 
 
 100 
 
 aoo 
 
 Gross Tons ( In 'OOO ) 
 
 In Fig. 13, surfaces and bars are used as alter- 
 native illustrations. The areas of the ships are 
 significant while the lengths of the bars are all that 
 need to be considered. Both illustrations are drawn 
 on absolute scales. The use of figures of ships is 
 
PRESENTING THE FACTS 
 
 79 
 
 suggestive, but the illustration is inconclusive because 
 of the absence of a scale and the use of two dimensions. 
 Notice the optical illusions in Fig. 14 : the bars seem 
 to be constricted at the black areas. The scale is unfor- 
 tunately placed at the right rather than at the left of 
 
 Fig. 
 
 14. — Cross-hatched bars showing the distribution of the 
 gross income of selected farmers in Wisconsin. 
 
 T&lae SappKed by the 
 Farm Toward Family'l 
 Living Bzpense (EeUmated) 
 
 FariDer's Labor Income 
 Unpaid Family Labor 
 
 Zuteieit on Inveatment 
 
 Depreciatlou of Bqalpment 
 
 Taxes and Insurance 
 
 Bepaira 
 
 lAiSG.Current Expenses 
 
 Feeds Parcbased 
 
 Hired Labor 
 
 1914 1916 1916 1917 Average 
 
 the figure. If faint guide lines were drawn across 
 the surface of the diagram, it would be easier to make 
 comparisons of the total and relative amounts. 
 
 Fig. 15 shows the percentage relationship between 
 the areas but does not give the concrete data upon 
 
80 STATISTICS IN BUSINESS 
 
 which the distribution is made. The cross-hatching 
 is distinctive. The bars, however, should have been 
 placed vertically. 
 
 Fig. 16 is distinctive in having both the concrete 
 data and the percentage relationships component parts 
 of the diagram. The order of the years is the reverse 
 of that followed in Figs. 14 and 15. 
 
 Fig. 15. — Cross-hatched bars showing the distribution of 
 areas on selected farms in Washington County, Ohio, 1912- 
 1916. 
 
 PER CENT 
 ZO 40 
 
 T 
 
 >3<^i^H^^^^^ 
 
 .9.3 ■■i^^^^^^^^^ 
 
 ^^m 
 
 1314 
 
 ^^^^mtmmm mm^mmmm sA 
 
 5-YEAR 
 AVERAGEl 
 
 wm^B^^^mmy///y/////y///.m^ 
 
 I CORN gta SMALL GRAIN ^Zl^^^Ki QJ MISCEL. CROf»S 
 
 In Fig. 17, a double percentage scale is used. The 
 shipments for each month of the year are shown 
 by the height of a rectangle. The [rectangles are 
 distinct, uniform in width, and broad enough to 
 be emphatic. Undoubtedly, the most evident thing 
 from the diagram is not the percentage amounts for 
 the months individually, but the general distribution 
 throughout the year. It would have been helpful in 
 the interpretation of the diagram, if the absolute 
 amount which is distributed on a percentage basis 
 throughout the year had been made a part of the illus- 
 
PRESENTING THE FACTS 
 
 81 
 
 tration. The accuracy of the distribution by months, 
 if not the exact amount shipped during the year, 
 could then have been proved. 
 
 Fig. 16. — Cross-hatched bars showing the per cent, distribu- 
 tion of stocks of sugar reported for August 31, 1917 and August 
 31, 1916 for important groups of firms. 
 
 10 
 
 20 
 
 1917 
 
 1916 
 
 Per Cent 
 « 50 60 70 
 
 80 
 
 so 100 
 
 Sugar and Storage 
 
 ilrap miUi warehouiea 
 and refineriei 
 
 MlBcellau- 
 eooA 
 
 Stocks Repoktbd (Pounds) 
 
 
 1917 
 
 1916 
 
 
 Quantity 
 
 Per cent. 
 
 Quantity 
 
 Per cent. 
 
 Total 
 
 1,039,279,301 
 
 100.0 
 
 1,430,660,470 
 
 100.0 
 
 Sugar and sirup mills 
 
 
 
 
 
 and refineries 
 
 480,767,457 
 
 46.3 
 
 660,301,064 
 
 46.2 
 
 Storage warehouses. . . 
 
 146,728,359 
 
 14.1 
 
 428,077,562 
 
 29.9 
 
 Wholesale grocers 
 
 207,398,679 
 
 20.0 
 
 166,961,829 
 
 11.7 
 
 Large users of sugar. . . 
 
 66,581,728 
 
 6.4 
 
 49,856,328 
 
 3.5 
 
 
 90,429,732 
 
 8.7 
 
 96,855,176 
 
 6.8 
 
 Miscellaneous 
 
 47,373,346 
 
 4.6 
 
 28,608,511 
 
 2.0 
 
 
 
 In Fig. 18, the bars are placed vertically and are 
 spaced on the horizontal axis in proportion to the 
 time. The figure is defective in not having a com- 
 mon scale. 
 
 In Fig. 19, the horizontal rectangular bars are 
 
82 STATISTICS IN BUSINESS 
 
 joined together thus giving a connected, step-like 
 curve covering the entire period. The widths of the 
 bars, moreover are proportionate to the periods be- 
 tween successive censuses. Contrast this illustration 
 and Fig. 18, which also depicts a fact historically. 
 Which do you prefer, a vertical or horizontal position 
 for the bars? 
 
 Fig. 17. — Bars stowing per cent distribution by months of 
 Cheddar cheese shipments from Wisconsin to Chicago, in 1911. 
 
 CHEDDAR CHEESE SHIPMENTS FROM WIS.TO CHICAGO ILL. 
 1911 
 
 I 
 
 T^ n 
 
 In Fig. 20, the wage groups for each class of wage 
 earners are represented on the horizontal axis by 
 vertical lines, uniformily spaced throughout the dia- 
 grams. It should be noted, however, that the rule 
 which requires the spaces to be proportionate to the 
 size of the groups is violated for the group "Under 
 $3.00," and for all groups above $16.00. The effect 
 of widening the spaces so as to make them propor- 
 tionate to the size of the groups both at the beginning 
 
PRESENTING THE FACTS 
 
 83 
 
 and the- end of the curves would be to give them a 
 flatter and more dispersed appearance. 
 
 The concrete data, here, as in so many diagrams, 
 unfortunately are missing. 
 
 Fig. 18. — Bar-diagram showing values of products in leading 
 industries, 1879-1913. (Values in millions of dollars.) 
 
 328' 
 
 ,33© 
 
 t85 
 
 168 
 
 137 
 
 S 
 s 
 
 to 
 23 
 
 BOOTS a SHOES 
 
 EXCWSIVB OP CUT STOCK 
 AND FINDINQS 
 
 THE TEXTILE INDOSTRIES 
 
 COTTON . WOOLEN . AND 
 
 WORSTED GOODS 
 
 The value of a frequency dot map, as illustrated 
 in Fig. 21, is that it gives a clear idea of density 
 and distribution, and change from "highs" to "lows." 
 It is easy from such a map to visualize places of con- 
 
84 
 
 STATISTICS IN BUSINESS 
 
 centration and " scatteration, " The value of each 
 dot is of Uttle consequence in reading exact frequency, 
 since the chief purpose of the map is only to give 
 an impressionistic view. 
 
 Fig. 19. — Oross-hatclied bars showing by census years, the pro- 
 portion of urban population to total population in Massachusetts, 
 1790-1910. 
 
 90 
 PER ecriT 
 
 The type of map illustrated in Fig. 22, is unsatis- 
 factory because the sizes of the dots are not readily 
 comparable. If it is not desired to show exact 
 amounts, then the scale is useless; if it is so desired, 
 the illustration fails of its purpose. 
 
PRESENTING THE FACTS 
 
 85 
 
 Such a map as that shown in Fig. 23, is unsatis- 
 factory; neither the size nor the shading of the dots 
 being readily comparable. 
 
 Fig. 20. — Frequency graphs showing the percentage wage distri- 
 bution of classified wage-earners by wage groups. 
 
 BOOTS AND SHOES 
 
 EXCLUSIVE OF CUT STXK AND RNDINQS. 
 
 
 D0t-l->^0^^ F^EF^ WEEK 
 
 THE TEXTILES 
 
 COTTON. WOOLEN. AND WORSTED GOODS. 
 
 In Fig. 27, the "bars are placed vertically .... and 
 the so-called 'curve' is formed by introducing the 
 line connecting the points at the end of the bars. 
 
86 
 
 STATISTICS IN BUSINESS 
 
PRESENTING THE FACTS 
 
 87 
 
 "Now it is evident that the only things properly comparable in 
 such a chart are the distances from the base line to the points 
 determined — in other words, the length of the bars. The intro- 
 duction of the distinctive connecting line at once diverts attention 
 from the proper comparison to the line itself. If, as is usually the 
 case, the bars be not introduced the gradient or steepness of the 
 line becomes then inevitably the basis of judgment and all notion 
 of the distances as the real subject of comparison is lost. Un- 
 consciously the line is erroneously interpreted as expressing rate 
 of change. But rate of change . . . .can only be accurately re- 
 
 FiG. 22. — Varying-size dot map showing amounts of primary 
 shipments of American Cheese from Wisconsin, 1911. 
 
 presented by a ratio chart in which percentage differences and 
 not arithmetic differences are plotted. 
 
 "Moreover, it often happens that a large part of the scale has 
 no points assigned to it. In that case it is common practice to 
 omit the lower portion of the scale. This at once and completely 
 renders impossible the only significant comparison. Suppose the 
 smallest magnitude in a given group be 75 and a larger magnitudje 
 be 100. It would then be in accord with common practice to cut 
 away the lower portion of the scale to, say, 70. The ocular com- 
 parison of the two magnitudes will now, of necessity, be that 
 
88 
 
 STATISTICS IN BUSINESS 
 
 between 5 and 30 and not between 75 and 100. The chart then 
 becomes not only useless but positively deceptive. Furthermore, ' 
 when the series of magnitudes or number of lines becomes increased 
 beyond two it becomes difficult, if not impossible, to compare the 
 
 Fig. 23. — Varying-shade dot map showing the amount of 
 dairy butter, in pounds, produced, sold, and consumed, in Wis- 
 consin Counties, 1909. 
 
 distances even though the entire scale be given. If this is further 
 complicated by an abbreviated scale the situation becomes one of 
 obscurity multiplied by deception." 
 
 Frequently, it is desired to show graphically per- 
 
PRESENTING THE FACTS 
 
 89 
 
90 
 
 STATISTICS IN BUSINESS 
 
PRESENTING THE FACTS 
 
 91 
 
 Fig. 26. — Bar-diagram showing the relative growth in investment 
 and in electricity sold in kilowatt hours, for years, 1896-1913. 
 
 »8(t,OCCI,000 
 
 MO^OOO.OOO 
 
 Ellowitt, HoDll.Sold I 
 DoIUlb oI Ju^aitjzieDt | 
 
 TU.OOO.OOO 
 
 Doo.ooo.gop 
 
 aa>,ooo,ooo| 
 
 am.ooojm 
 
 120 ,000 .dot 
 
 1S97 .1S0« lOQI 1001 lOOS 1907 ISOO 10)1 Jill 
 
 Fig. 27. — Combination bar-diagram and line chart. 
 
92 STATISTICS IN BUSINESS 
 
 centage rather than absolute changes. The ordinary 
 graphs, such as those above, show absolute changes or 
 differences. When percentages are to be shown, a 
 "ratio," or logarithmic scale, must be used. Arith- 
 metic or difference scales and percentage or ratio 
 scales are illustrated and described immediately below 
 in an article prepared by Lucian W. Chaney. 
 
 Arithmetic Scale 
 10 15 20 30 40 » 60 
 
 Percentaec Scale 
 ^0 y 20 W 80 IM MO 
 
 "It will be noted that in the arithmetic scale equal linear 
 distances represent equal arithmetic differences, whereas in the 
 percentage scale equal linear distances express equal percentage 
 differences. In the case of the arithmetic scale one space repre- 
 sents 10 units; in the percentage scale one space represents 100 
 per cent, difference. 
 
 "If it is desired to introduce intermediate numbers in the above 
 arithmetic scale, the space between any two of these will be 
 divided into 10 equal parts. Eleven would then be one unit from 
 10, while 15 would be midway between 10 and 20, since points 
 having equal arithmetic differences are alwajra equidistant. The 
 construction of a complete percentage scale, on the other hand, is 
 more complicated because the relation of any magnitude as com- 
 pared with an ascending or descending series of magnitudes is a 
 constantly changing percentage. To illustrate: From 100 to 
 110 is a 10 per cent, increase, whereas from 200 to 210 the increase 
 is only 5 per cent. Therefore, on a percentage scale the linear 
 distance from 200 to 210 wiU be less than that from 100 to 110. 
 Thus it is seen that in passing up the percentage scale numbers 
 separated hy the same difference as regards magnitude will be 
 represented as drawing closer together on account of the decreasing 
 porcentage of difference. 
 
 "Suppose it is desired to locate the intermediate number 15 
 on the percentage scale given above. In order to do this the fun- 
 damental method is to find from logarithmic tables the logarithms 
 
PRESENTING THE FACTS 
 
 93 
 
 - °£li S 
 
94 STATISTICS IN BUSINESS 
 
 of 10, 15, and 20 and then place 15 in a position representing the 
 relation between its logarithm and those of 10 and 20. When this 
 is done it wiU be found that 15 is not equally distant from 10 and 
 20 as in the arithmetic scale, but is nearer to 20, as shown. This 
 accords with the fact already shown by illustration that the 
 relation of a given value to an increasing series is a constantly 
 decreasing percentage." 
 
 It is, of course, unnecessary to prepare your own 
 ratio paper, since various types may be secured in the 
 trade. Figs. 28 and 29, respectively, taken from 
 Fisher, "The 'Ratio' Chart," show the population of 
 the United States plotted on a ratio and on a differ- 
 ence basis. 
 
 Professor Chaney has the following to say concern- 
 ing the characteristics and functions of the "ratio" 
 chart. 
 
 " 1. In a ratio chart a given linear distance on the scale always 
 represents the same percentage difference. 
 
 "2. The gradient or steepness of the lines always and inevitably 
 expresses the exact rate of change in any series of statistical facts. 
 Consequently, equal rates of change or equal percentages of differ- 
 ence will have the same gradients. If two magnitudes vary 10 
 per cent, upward their curves will run parallel however far sepa- 
 rated they may be on the chart. For example, if one magnitude 
 increases from 10 to 11 while another increases from 100 to 110 
 the curves corresponding to the change will be parallel, indicating 
 the same rate of change. It is evident that plotting the same 
 magnitudes on an arithmetic scale would show ten times the 
 amount of difference in the second case although the percentage 
 difference is identical. 
 
 "3. The percentage scale in the ratio chart has no zero. 
 A moment's consideration will show that this must necessarily be 
 true. As long as there are magnitudes to be plotted, no matter 
 how small, the percentage decrease can never be 100 and thus 
 can never theoretically reach the zero point. . . . The absence 
 of the zero in the ratio chart is sometimes misapprehended as a 
 
PRESENTING THE FACTS 
 
 95 
 
 disadvantage. On the contrary, the particular value of the scale 
 is related to this fact. Because of the absence of the zero, atten- 
 
 o 
 
 T-H 
 
 o 
 
 i 
 
 03 
 
 Ul 
 
 D 
 o 
 
 3 
 P. 
 O 
 P. 
 
 o 
 
 .3 
 
 A 
 
 CI 
 '% 
 
 o 
 
 O 
 
 C3 
 
 £5|g g g g g 
 
 o o o o o 
 
 lO -.]• CO N W 
 
 
 
 s 
 
 
 L 
 
 
 ^^ 
 
 
 s 
 
 
 ;:::— -^--- 
 
 
 
 
 !s : 
 
 
 
 
 I" 
 
 
 
 
 
 s 
 
 
 A - 
 
 
 3 
 
 
 - ^- 
 
 
 - A 
 
 
 
 
 " \ 
 
 
 L 
 
 
 -i::^::::::: 
 
 
 
 
 C - 
 
 
 1 
 
 
 
 
 
 
 I 
 
 
 T 
 
 
 
 
 I S 
 
 
 _ _ !S- - 
 
 
 C " 
 
 
 -\ 
 
 
 
 
 
 
 
 
 r 
 
 
 r 
 
 
 t " 
 
 
 i " 
 
 
 " 
 
 
 
 
 
 
 
 
 
 
 r" 
 
 
 I 
 
 
 - 4- 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 fin 
 
 
 0> GO tv <tf 
 
 tion is necessaniy ana properly centered upon the relations of the 
 various magnitudes to each other and particularly upon the rates 
 of change. 
 
96 STATISTICS IN BUSINESS 
 
 " 4. The ratio chart makes possible a direct and correct com- 
 parison of increases and dechnes. The usual method of expressing 
 changes up or down is to say, for example, that a rise of 50 per 
 cent, was followed by a decline of 30 per cent. This mode of 
 expression is used without realization that it involves expressions 
 which cannot be compared one with the other. Comparatively 
 few persons at once recognize that an increase of 100 percent, is 
 exactly balanced by a decline of 50 per cent. Percentages of 
 increase can be properly compared with other percentages of the 
 same sort and percentages of decline are similarly comparable, 
 but no direct comparison can be made between a percentage of 
 increase and a percentage of dechne." 
 
CHAPTER VI 
 
 SUMMARIZING THE FACTS— AVERAGES AND 
 OTHER MEANS 
 
 The viewpoint of the business man who is willing 
 to act on the basis of facts is, What does the analysis 
 show? To what conclusions does it lead? The 
 demand is for some form of a summarized statement. 
 The details must be shortened, or crowded together 
 into a single expression. Not that they are of no 
 significance, but as details they are impossible of 
 being readily handled. A total which summarizes 
 the different parts, or an average which seems to 
 characterize the detail, and which can be compared 
 with similar figures over a period, or for different 
 conditions, is what is wanted. 
 
 Men of action are sometimes impatient with details 
 and treat them as though they were identical and 
 uniform, and could be ignored. They are inclined to 
 look upon them as "details," which will take care of 
 themselves. This attitude is suggestive of the state 
 of mind which looks upon business as simple, and its 
 processes as capable of being reduced to a few under- 
 lying principles, which can better be felt than stated; 
 better expressed as axioms than as relative truths. 
 The point of view is what may be termed absolute 
 rather than relative. It looks with suspicion upon 
 diagnosis, and is rather content with generalization. 
 It tends to ignore the fundamental truth that busi- 
 
 7 97 
 
98 STATISTICS IN BUSINESS 
 
 ness is diverse and the situations with which it deals 
 ever changing, and to accept the dogma of status. 
 It is impatient, for instance, with the idea that labor 
 is more than a commodity, that the market cannot be 
 stated in single terms of "demand and supply," 
 and that a protective tariff, competition, or free trade 
 have limitations depending upon the type of national 
 industry, necessity for state control, and the interests 
 of classes. 
 
 Now, this type of mind has both its strength and 
 limitations. There are a comparatively few funda- 
 mental underlying business truths resting on human 
 psychology, the extent of industrial development, 
 etc., but they are relative for time and place, and 
 are not absolute. They are discovered not by intui- 
 tion, but by analysis. Neither can they be divorced 
 entirely from the detail of business operation, trade 
 relation, and human conduct. Average market 
 conditions may be accurately stated. Likewise the 
 response of the average individual to a type of adver- 
 tising, for instance, may be calculated. Business, 
 while it can not overlook these underlying truths, can- 
 not always be sure that a particular unit will benefit 
 or suffer from them. All of the conditions which give 
 rise to them may not be experienced in every busi- 
 ness. There are some which are above and some which 
 are below the norm established for business as a 
 whole. For instance, it may be true that costs vary 
 with industrial output, but the rate is different for 
 different producing establishments. The business 
 which is built on a general cost basis, will have diffi- 
 culty, under certain conditions, in financing its opera- 
 
SUMMARIZING THE FACTS 99 
 
 tions; and, under other conditions, will be realizing 
 enormous profits. 
 
 The point which it is desired to emphasize is that 
 there are variations, among individual businesses, 
 from the norm established by business as a whole, and 
 these should not be lost sight of in the daily conditions 
 of operation. A business unit, large or small, must 
 shape its policy on its past experience and on the 
 experience of business as a whole, but it cannot be 
 blind to the fact that most, if not all, of these are 
 relative only, and that new conditions and new prob- 
 lems are always suggesting and making necessary 
 changes and readjustments. 
 
 What has been said has particular application to the 
 subject of this chapter. Averages, in the terms of 
 which business is wont to express its condition and to 
 compare its operations, should not be regarded as "a 
 secret something which determiaes events ..." 
 After calculating a certain average, business is likely 
 to conclude that some secret fate is at work and to 
 expect a faithful and continuous repetition of this 
 average. Every average is a sort of fictitious substi- 
 tute for the details which it replaces, serviceable when 
 the conditions for which it stands are known, but 
 deceptive when they are ignored. 
 
 The truth of this contention should be seen more 
 concretely. Business profits may be stated as aver- 
 ages. In this form they are convenient., A statement 
 of the average wage which is paid to a diverse labbr 
 force may carry some meaning to the business execu- 
 tive. Likewise, costs over a period of time may be 
 averaged in order to detect improvement, or the reverse. 
 But profits are different on different goods. On 
 
100 STATISTICS IN BUSINESS 
 
 one the mark-up is 20 per cent.; on another 50 per 
 cent. On one the turn-over per year is ten; on the 
 other, two. Can these differences be ignored in the 
 single expression "average profits?" Likewise, the 
 average wage paid may, for comparative purposes, be 
 a satisfactory way of stating the wage bill; but is it 
 significant in meeting the demands, on the part of 
 labor representatives, for increased wages, or satis- 
 factory to the employer in contrasting amounts paid 
 and services secured? Similarly, average costs are 
 deceptive unless the conditions of their measurement 
 are identical. 
 
 The burden of what has just been said is that 
 general impressions, whether expressed as averages or 
 otherwise, will not suffice in business. Averages con- 
 stitute norms with which experience may be compared, 
 but comparison is valid only when conditions are 
 identical. It is a legitimate endeavor of business to 
 set up for different types of enterprises norms or 
 average conditions which will serve as guides in test- 
 ing operations. However, these standards must be 
 precise, and the conditions to which they apply, 
 uniform. For many purposes, the differences from 
 the average are far more significant than the norm 
 itself, since they measure the relative degree with 
 which it is experienced. 
 
 Let us apply what has been said to the different 
 type? of averages which should be used in the analysis 
 of biisiness problems. 
 
 First, there is the generally known arithmetic 
 mean, or average. It is on the tongue of every busi- 
 ness man, and is probably the most generally used 
 summary expression. What does it mean? It is 
 
SUMMARIZING THE FACTS 101 
 
 that amount which results from dividing the sum of a 
 series of numbers by the number in the series. Spe- 
 cifically, the average sale from the following experi- 
 ence— $1.00, $5.00, $3.28, $.60, $2.22, $4.81, $.10— is 
 $2.43. What is this average? Plainly, it is the center 
 of gravity, or balancing point in the series, the numbers 
 larger than it being exactly balanced by those smaller 
 than it. It is clearly not represented in the series 
 at all. In this sense, it is purely fictitious. It is 
 unreal. In another series, however, this average may 
 be represented in every number, as in the series $2.43, 
 $2.43, $2.43, $2.43; average $2.43. In still another, 
 it may be closely approached by some of the items 
 and widely separated from others, as in the series, 
 $2.39, $2.41, $2.45, $2.46, $.10, $.15, $9.62, $.26, 
 $2.03; average $2.43. 
 
 What are its characteristics? First, all of the items 
 have to be included in the computation. Second, all 
 of the items, though different, are treated as identical 
 in the divisor. Third, it is not of necessity, though 
 it may be, represented in a series. Fourth, in giving 
 the result, each item is significant according to its 
 size. 
 
 The average (arithmetic mean) as such, tells one 
 nothing concerning the series out of which it is made. 
 The differences from it may be large or small; how 
 large or how small is not known. It ignores the 
 detail. It groups different conditions together, and 
 reduces them to a hypothetical common denominator 
 by an arbitrary process of division. 
 
 Are business operations, or experience, or groups 
 of them, capable for practical purposes of being so 
 described? What is needed is not a purely hypo- 
 
102 STATISTICS IN BUSINESS 
 
 thetical center of gravity, which the average gives, but 
 a description of the differences from the average, and 
 the manner in which they are distributed about it. 
 Take, for example, wages or transportation costs. 
 What is needed adequately to express either, so as to 
 set them in their true light for business planning and 
 the solution of the problems to which they give rise, 
 is some measure of their distribution for the same or 
 for different classes. What are the extremes; what 
 is the most common wage or cost; above or below 
 what figure do the bulk of the instances fall? 
 What is the average difference from the average, and 
 to what are the wide differences due? 
 
 When doubt arises as to details, appeal is made to 
 averages. They have been called the business man's 
 excuse for laziness. They might also be called the 
 device par excellence, for dealing in glittering generali- 
 ties. As averages are often used, both indictments 
 are, without doubt, largely true. The scientific point 
 of view does not require that averages be repudiated, 
 but it does provide that they shall be used with in- 
 telligence and discrimination. 
 
 However, there are many significant uses of the 
 aveiage (arithmetic mean). Statistics has been called 
 by some the "science of averages," and appeal is 
 often made to the "law of averages." What is this 
 law? Business and other experiences tell us that it 
 is unnecessary in many problems to measure all of a 
 series or to count all of the instances with which we 
 deal. Not all butter is sampled when purchased, 
 nor all cotton scrutinized when graded. In an analy- 
 sis of markets, appeal may be made to the law of 
 averages. In keeping with the general principle that 
 
SUMMARIZING THE FACTS 103 
 
 the average height of a number of people may be 
 secured by studying the heights of a few thousand 
 drawn at random from a larger body, the response to 
 a selling or advertising campaign, for instance, may 
 be established from an analysis of a well selected 
 group of samples. It is unnecessary to include every- 
 body, but it is essential that each characteristic of 
 the group shall be represented in the samples taken. 
 Realizing this fact, business enterprises are appealing 
 to the law of averages in studying markets and in 
 testing advertising media. How truly samples may 
 be representative, however, is often times difficult to 
 establish. Scientific observation may be difficult. 
 The peculiarities of a group may not be revealed 
 from the samples taken, and serious error result 
 from generalizing broadly from samples which can be 
 measured. 
 
 The value of sampling as a method is conditioned 
 by the degree to which a part represents a whole. 
 Too frequently samples are employed with the belief 
 that "other things will remain equal." In measuring 
 physical phenomena, the most accurate result may 
 be secured by averaging all measurements, if there is 
 no bias in the unit of measurement, if allowance is 
 made for the personal equation, and if measurements 
 are made under similar conditions. Business phenom- 
 ena, however, are constantly changing. Samples 
 which will suffice in one period wiU be inadequate at 
 another. Conditions of time, place and income, as 
 well as the psychology of the groups to which the meas- 
 urements apply, are constantly in a state of flux, and 
 one should not place too much reliance in the compen- 
 sation of errors. Business conditions change with 
 
104 STATISTICS IN BUSINESS 
 
 the temper of the people, with political practices and 
 principles, with labor unrest, etc. Blindly, to take 
 an average in the hope that the law of compensating 
 errors will always give a perfect picture from imperfect 
 detail is economically suicidal. 
 
 The peculiarities of the arithmetic mean, as an 
 average, cannot be removed. All of the items which 
 enter into it are given equal weight; they are all 
 treated the same in the divisor, and the product of 
 the division is almost invariably hypothetical. As a 
 single summary figure, it is often unsatisfactory. In 
 time comparisons, it is generally misleading if the 
 data out of which it grows are not homogeneous. 
 The same is equally true when it is applied to geo- 
 graphical or frequency data. An average of this type 
 may not only be unrepresentative but deceptive. 
 The average daily output of a factory over a period 
 may remain constant and yet the production in 
 various departments change radically. Similarly, 
 the average wage paid may remain constant and the 
 wage scale seriously slump or rise at the lower, middle 
 or upper groups. 
 
 But there are, of course, other averages. These, 
 however, are less commonly used, although for many 
 purposes they are superior to the arithmetic mean. 
 They are averages, however, and are subject to many 
 of the limitations which are characteristic of the 
 arithmetic mean. 
 
 Probably the most familiar of the other ways of 
 characterizing complex details, is to use the median. 
 The median is the middle item in a series arranged 
 in the order of size, and divides the group, therefore, 
 into two parts. In this sense, undoubtedly, it is 
 
SUMMARIZING THE FACTS 105 
 
 more accurately described as a partition expression 
 or division mark, although it serves the purpose of 
 an average. Similarly, it is possible to divide a series 
 into more than two parts. In case the division is 
 into four parts, the partition expressions are known 
 as quartiles. 
 
 What are the characteristics of the median? 
 
 First. — In its computation, all of the data are 
 required, but the frequencies only are important and 
 not the size of the items, except at or near the middle. 
 
 Second. — It is uncertain and indefinite in a series 
 which is not essentially homogeneous. That is, a 
 series may be uniform throughout, as, for instance, 
 in the case of the wage-rates of a group of 100 indi- 
 viduals. The median of such a series would be the 
 characteristic wage-rate; as would also the arithmetic 
 mean. However, if a few poorly paid individuals 
 were introduced at the lower side, and a few highly 
 paid persons at the upper side, the median would 
 remain the same, but the arithmetic mean would be 
 different. 
 
 Third. — ^The median may be computed when the 
 size of the items at the extremes is unknown, pro- 
 vided the frequencies are given. This is of distinct 
 advantage when the measurements are imperfect, or 
 incapable of being known. 
 
 Fourth. — The median may be indeterminate. It 
 may fall between two measurements in a series. In 
 such a case, it is, like the arithmetic mean, a purely 
 fictitious number. 
 
 If business men, in their attempt to summarize 
 the detailed facts of their business, would use both 
 the arithmetic mean and the median, there would be 
 
106 STATISTICS IN BUSINESS 
 
 less tendency for their generalizations to be loose 
 and indefinite, since the two figures would supplement 
 each other. However, the median, because of its 
 peculiar meaning, is frequently unconsciously used. 
 Wage earners, for instance, are ranked according to 
 their honesty, integrity, and industry; and standards 
 are set which apply not to the exceptionally good 
 man, nor to the exceptionally poor man, but rather 
 to the middle man, thought of in comparative terms. 
 Psychologists, in the selection of employees by mental 
 tests, or by other means, frequently employ the 
 median, and relate individuals in a series to this 
 middle man. Wherever the ranking device is em- 
 ployed, the median concept is used. 
 
 Moreover, the arithmetic mean and the median of 
 details which are not too erratic and dissimilar tend 
 closeily to agree. The arithmetic mean, because of its 
 being affected by the extremes as well as by the fre- 
 quencies, tends to be less than the median when the 
 small items predominate, and larger than the median 
 when large ones are more frequent. 
 • If the arithmetic mean wage, or cost, is compared 
 not only with the median, but also with the quarter 
 measures, or quartiles, then as a summary expression, 
 it becomes more significant than when it stands alone. 
 The point was made in the discussion of the arithmetic 
 mean, that it lacks definiteness, and is often used 
 loosely to describe a situation which cannot be sum- 
 marized in a single figure. If it is compared with the 
 median and quartiles, as averages, then a part at least 
 of this criticism no longer applies. If the business 
 executive keeps in mind the purposes which averages 
 seiVe, and the necessity for' business facts to be sum- 
 
SUMMARIZING THE FACTS 
 
 107 
 
 marized in brief form, he should be anxious to employ 
 not only one but several devices which serve his 
 purpose. 
 
 The use of the median in connection with an ordi- 
 nary payroll may be illustrated, the purpose of the 
 average (the median) being to characterize the hourly 
 wage-rates which are paid. The number of men and 
 the wage-rates per hour are given below: 
 
 Table 10. — Table Showing Distribution op Houelt Wage-rates 
 
 Number of men 
 
 Wage-rates per 
 hour, cents 
 
 Number of men 
 
 Wage-rates per 
 hour, cents 
 
 12 
 16 
 25 
 
 60 
 70 
 75 
 
 9 
 
 4 
 2 
 
 82 
 90 
 95 
 
 The arithmetic wage-rate is 73.6 cents and the median 
 75 cents. It will be noticed that the order of arrange- 
 ment is consecutive, and that the median rate is 1.4 
 cents more than the average. The wage-rate of the 
 individual one-quarter of the way up the series is 70 
 cents and that of the individual three-quarters of the 
 way up the series is 75 cents. In the median and 
 two quartiles, therefore, we have three summarizing 
 expressions of this series. The arithmetic mean, on 
 the other hand, gives us but one. 
 
 There is still another average, which is in current use, 
 and which should be employed in business. It is 
 what is called the mode. It is that item in a series 
 which is most characteristic, or common. It is the 
 typical fact, and being typical, is representative. It 
 is in no sense hypothetical or unreal. It is that posi- 
 tion where most of the instances fall, and which may 
 
108 STATISTICS IN BUSINESS 
 
 be said to be characteristic. In the above series show- 
 ing the wage-rates for men, more individuals were 
 shown to have been receiving 75 cents than any other 
 amount; 75 cents is, therefore, the mode. Of course, 
 there were people receiving more and others receiving 
 less than this amount, but these, for the purpose of 
 this particular summarizing expression are ignored. 
 
 What are the characteristics of the mode as an 
 average? 
 
 First. — Only a part of the data is required for its 
 computation. In the series above, the mode would 
 have been no different had the two people who are 
 shown to have received 95 cents, received $2.00. 
 Similarly, it would have remained the same had the 
 twelve people, who are shown to have received 60 cents, 
 per hour, received purely a nominal sum. 
 
 Second. — The mode as an average is invariably rep- 
 resented in a series. 
 
 Third. — In the calculation of the mode, the frequen- 
 cies, or number of instances, are primary, and the units 
 to which the frequencies occur, only secondary. 
 
 In the discussion of business success and failure, 
 labor force, cost, etc., when these are summarized in a 
 single expression, undoubtedly, the mode is the average 
 which is most commonly in mind. The modal idea is 
 expressed in the "average" clerk, the "average" bank 
 clearing, the "average" day's sale, the "average" 
 man on the street. That is, the thing which is the 
 rule, or which is characteristic, is expressed in this 
 way. It is the prevailing rate, or individual, which is 
 in mind. 
 
 Fourth. — Extreme items are ignored. 
 
SUMMARIZING THE FACTS 109 
 
 Fifth. — Its location is sometimes indeterminate. 
 There may be more than one mode, in case the series 
 is complex. 
 
 The mode, like the median, is different from the 
 arithmetic mean, inasmuch as extreme items, or in- 
 stances, are ignored. The mode tends to remain fixed, 
 is less erratic than the median, and far less subject 
 to change than the arithmetic mean. When taken to- 
 gether, these three averages serve rather fully to 
 describe the detail concerning any business fact. 
 Taken alone, either of them is indefinite and a poor 
 substitute for the detail which they replace. 
 
 There is no reason why business should not become 
 as familiar with the use both of the median and the 
 mode, as it is with the arithmetic mean; and there is 
 far greater justification in many instances for the use 
 of the mode as a single expression, than there is for the 
 use of the arithmetic mean. The business executive 
 should not "rush headlong," as it were, into the use 
 of any of these averages, without an appreciation of 
 the relationship which they have to his precise problems, 
 and without a keen appreciation of the characteristics 
 which each possesses. Each of them is designed to put 
 into brief form, for the purpose of comparison, the 
 essence of the detail to which it relates. They should 
 be used to give expression to a conclusion arrived at 
 from the study of details, and this cannot be done un- 
 less the precise nature of each one is thoroughly under- 
 stood. To employ averages to express the result of a 
 process of thought or analysis, is always legitimate 
 when they are used discriminatingly. 
 
 No single average is good for all purposes. Each is 
 affected differently by the arrangement, frequencies, 
 
110 STATISTICS IN BUSINESS 
 
 and the character of the details, and should be em- 
 ployed with a full knowledge of its peculiarities. The 
 use of an average is always a function of the purpose 
 which one has in mind. The form of the average and 
 its use cannot be divorced. Caution and foresight are 
 necessary at every step in the use of averages; caution 
 as to those which are to be employed; foresight as to 
 the significance which they have, and analysis as to 
 the possibility of details to be characterized in such a 
 manner. To use them blindly, and without discrimi- 
 nation, is in violation of the underlying principles 
 of scientific method as applied to business problems. 
 The executive, no matter how large or how small the 
 business he controls may be, or in whatever fields he 
 may be working, cannot afford to base his judgment 
 on averages without a keen appreciation of what is 
 implied in doing so. 
 
 In the use of averages for business purposes, the 
 following questions should be raised and answered. 
 Is it possible to employ a single expression to depict 
 the details which are essential so as to view data in 
 all their bearings? In the problem considered, is the 
 greatest interest in the characteristic or modal feature, 
 in the median or half-way position or in that mathe- 
 matical position at which the average (arithmetic 
 mean) falls? Is it necessary and wise to employ all 
 of these descriptive units, to compare their differences 
 and to determine their similarities? No single an- 
 swer to these questions can be given. To employ an 
 average may be legitimate, and still the question be 
 indeterminate as to the most appropriate average to 
 use. Data must be analyzed and the functions of 
 averages in general and in particular be clearly per- 
 
SUMMARIZING THE FACTS 111 
 
 ceived before answers can be given. As caution and 
 analysis are necessary in the use of averages, so dis- 
 crimination and judgment are essential in assigning 
 importance to them when used. 
 
 In no other aspect of business is the employment of 
 an average so common and at the same time its use 
 so little understood, as in summarizing prices. Sum- 
 maries are wanted for prices of labor, money, mate- 
 rials, securities, etc. To know the market condition 
 and trend is imperative for business operation and 
 planning. But prices differ for different goods or 
 services, different conditions of demand and supply, 
 different markets, different conditions of sale and 
 purchase. The meaning of price change is different 
 for differently situated producers, consumers, and 
 middlemen. For instance, an economist may use 
 stock prices "to measure change in the purchasing 
 power of money over stocks; a speculator may wish 
 to forecast the probable future course of the market; 
 a public commission may be interested in the terms 
 on which corporations can raise new capital; a pub- 
 licist may investigate the claim that government regu- 
 lation has brought loss upon investors; a financial 
 historian may wish to mark off periods of expansion 
 and contraction; a trustee may inquire whether the 
 fluctuations of his security holdings have compared 
 favorably with the average course of the market; an 
 insurance company may seek light on the probable 
 future of interest rates; a student may wish to com- 
 pare stock speculations with the price fluctuations of 
 commodities at wholesale or retail, of labor, of bonds, 
 of farm lands, of securities in other countries, etc. 
 Now, each of these people will have use for a stock 
 
112 STATISTICS IN BUSINESS 
 
 index. But the more carefully these various uses are 
 analyzed, the clearer it becomes that their require- 
 ments differ. " The prices of commodities, wholesale 
 and retail, are wanted for as varied uses, as are 
 also those of the prices of labor. How are prices 
 to be summarized and interpreted for these different 
 purposes? 
 
 Business men and students of economics are famil- 
 iar with the currently compiled indexes of prices. They 
 at least know by name Bradstreet's, Dun's, The An- 
 nalist's and the Bureau of Labor's index numbers. 
 But do they know what they contain, what they mean, 
 and are they consistent in their use of them in con- 
 nection with price problems? Is their attitude toward 
 them scientific, or rule-of -thumb? How discriminat- 
 ing are they in quoting authorities, and how consist- 
 ent in using them as a basis for business policies and 
 conclusions? 
 
 Index numbers in the simplest form may be defined 
 as relative or percentage numbers in which data for 
 one year or other similar period, or an average for a 
 year or such period, are taken as a base, generally 
 indicated by 100, and upon which data for subsequent 
 years or periods are computed as percentages. The 
 method by which a simple index number of prices 
 may be calculated is illustrated below. 
 
 What has been the movement of the prices of build- 
 ing material during the war? In this illustration, 
 only a few quotations are taken, and the index num- 
 bers would not suffice for too broad a generalization. 
 However, it is the principle of index number making 
 which is now being discussed and these prices will 
 suffice for this purpose. 
 
SUMMARIZING THE PACTS 
 
 113 
 
 Table 11. — Absoltttb and Relative Wholesale Prices op Build- 
 ing Materials, 1913 to 1919' 
 
 Actual Prices 
 
 
 Average wholesale prices in 
 
 Commodity quotation 
 
 
 group 
 
 
 
 
 
 
 
 
 1913 
 
 1914 
 
 1915 
 
 1916 
 
 1917 
 
 1918 
 
 1. Clay Products 
 
 
 
 
 
 
 
 (o) Brick, Common Build- 
 
 
 
 
 
 
 
 ing (New York City) 
 
 
 
 
 
 
 
 per M 
 
 $6 .6300 
 
 $5 . 8467 
 
 $5.9425 
 
 $7.7267 
 
 $8 .8933 
 
 SIO 8975 
 
 (!>) Sewer pipe, salt glazed 
 
 
 
 
 
 
 VA^.f -Ufl \J 
 
 fire clay, 6 in. (N. E. 
 
 
 
 
 
 
 
 U. S.) per linear ft. .. .. 
 
 .0558 
 
 0.0633 
 
 .0638 
 
 0.0704 
 
 0.0750 
 
 .0800 
 
 2. Quarry Products 
 
 
 
 
 
 
 
 (c) Indiana Lime stone. 
 
 
 
 
 
 
 
 buff, rough block (U. S.) 
 
 
 
 
 
 
 
 per cu. ft 
 
 .2500 
 
 0.2500 
 
 0.2500 
 
 0.2625 
 
 0.3583 
 
 .4208 
 
 (d) Lime in bulk (Chicago) 
 
 
 
 
 
 
 
 per short ton 
 
 4 .3750 
 
 4.0000 
 
 3.5000 
 
 4 .3750 
 
 6.1667 
 
 7.2500 
 
 3. Cement 
 
 
 (e) Portland cement (N. Y. 
 
 
 
 
 
 
 
 and N. Eng. States) per 
 
 
 
 
 
 
 
 bbl 
 
 1.0442 
 
 1.0500 
 
 0.8142 
 
 1 .0342 
 
 1 .3358 
 
 1 .6733 
 
 (J) Portland cement (111.) 
 
 
 per bbl 
 
 .9906 
 
 0.9052 
 
 0.8821 
 
 1.1144 
 
 1 .3975 
 
 1 .5500 
 
 4. GUss 
 
 
 (ff) Window glass, single 
 
 
 
 
 
 
 
 united, inches, 40-A 
 
 
 
 
 
 
 
 (N. Y.)per50sq.ft 
 
 2.5500 
 
 2 .55e0 
 
 2 .8050 
 
 3.4650 
 
 4.5353 
 
 6.7908 
 
 6. Lumber 
 
 
 
 
 
 
 
 (A) Southern yellow pine. 
 
 
 
 
 
 
 - 
 
 Finish B, and better. 
 
 
 
 
 
 
 
 6 in. and wider (Ala., 
 
 
 
 
 
 
 Ark., La., Tex., Miss.) 
 
 
 
 
 
 
 
 per M. ft 
 
 25.0312 
 
 23 .2227 
 
 22 .0422 
 
 24.6016 
 
 33.6094 
 
 37 .8906 
 
 (») Eastern hemlock, No. I 
 
 
 boards, S-l-S, I" X 8", 
 
 
 
 
 
 
 
 16' (Mich, and Wis.) per 
 
 
 
 
 
 
 
 M.ft 
 
 20.4445 
 
 18.8333 
 
 18.1667 
 
 21 .4792 
 
 27.6458 
 
 31.1042 
 
 6. Paints 
 
 
 Cj) Paint pigments, dry 
 
 
 
 
 
 
 
 colors, ocher (N. Y.) per 
 
 
 
 
 
 
 
 ton 
 
 12 .0000 
 
 12 .0000 
 
 13.0000 
 
 18.8333 
 
 21 .3333 
 
 30 .0000 
 
 
 
 ' Price Bulletin (various) War Industries Board, Washington, D. C, 
 1919. 
 
114 
 
 STATISTICS IN BUSINESS 
 
 Relative Prices 
 1913 = 100 
 
 Total of relatives 
 
 1000 .0 
 
 969.9 
 
 946.2 
 
 1155.4 
 
 1447.1 
 
 1778 .4 
 
 
 
 Index numbers as averages of 
 relative prices 
 
 100.0 
 
 97.0 
 
 94.6 
 
 115.5 
 
 144.7 
 
 177.8 
 
 
 
 
 100.0 
 100.0 
 100.0 
 100.0 
 100.0 
 100.0 
 100.0 
 100.0 
 100.0 
 100.0 
 
 88.2 
 113.5 
 100.0 
 
 91.4 
 100.5 
 
 91.4 
 100.0 
 
 92.8 
 
 92.1 
 100.0 
 
 89.6 
 
 114.3 
 
 100.0 
 
 80.0 
 
 78.0 
 
 89.0 
 
 110.0 
 
 88.1 
 
 88.9 
 
 108.3 
 
 116.5 
 126.2 
 105.0 
 100.0 
 
 99.0 
 112.5 
 135.9 
 
 98.3 
 105.1 
 156.9 
 
 134.1 
 134.5 
 143.3 
 141.0 
 127.9 
 141.1 
 177.9 
 134.3 
 135.2 
 177.8 
 
 164.4 
 
 
 143.4 
 
 2 — c as above 
 
 168.3 
 
 2 — d as above ^ . . . . 
 
 165.7 
 160.2 
 
 3 — ■/ as above 
 
 156.5 
 
 
 266.3 
 
 
 151.4 
 
 
 152.2 
 
 
 250.0 
 
 
 
 According to this calculation, prices of building 
 materials for the years 1913 to 1918 inclusive, ad- 
 vanced as follows: 
 
 
 Index number 
 
 Per cent, increase 
 
 
 Over 1913 
 
 Over preceding year 
 
 1913 
 
 100.0 
 97.0 
 94.6 
 115.5 
 144.7 
 177.8 
 
 3.0* 
 5.4* 
 15.5 
 
 44.7 
 77.8 
 
 
 1914 
 
 3.0* 
 
 1915 
 
 2 5* 
 
 1916 
 
 22 1 
 
 1917 
 
 25 3 
 
 1918 
 
 22 9 
 
 
 
 * Decrease. 
 
 This simple example contains the essential steps in 
 the calculation of an average of relative prices type of 
 index number. More important than the arithmetical 
 calculation is the selection of prices or other data to be 
 compared. Indeed, this is the major consideration 
 in making index numbers. After all, the purpose in 
 
SUMMARIZING THE FACTS 115 
 
 calculating them is to make a comparison, and the 
 validity of the inference drawn from them is deter- 
 mined not only by the method in which they are com- 
 bined, but also by the fact of their inherent likeness. 
 The truth that like can be compared only with like 
 applies here with especial emphasis. 
 
 In calculating and using an index number, busi- 
 ness executives should have in mind : 
 
 First. — The purpose for which the results are to be 
 used. 
 
 Second. — The number and kind of commodities 
 that are to be included, the form in which their prices 
 are stated, and the markets from which the quota- 
 tions are secured. 
 
 Third. — The questions as to whether all commodi- 
 ties are to be treated as equal, or are to be given 
 different weights. 
 
 Fourth. — The test to be used in assigning different 
 weights. 
 
 Fifth. — The base period against which comparisons 
 are to be made. 
 
 Sixth. — If averages of relative prices are used, the 
 average which should be chosen. 
 
 These conditions are important since not all index 
 numbers are equally well suited for all purposes. If 
 an executive wishes to calculate the effect on his em- 
 ployees of the increased cost of living, he ought not 
 to choose wholesale prices as a basis for an index series. 
 Moreover, the number of commodities which enter into 
 the index numbers and the importance assigned to 
 them, for this purpose, are important. Prices of a 
 half-dozen commodities purchased in large quantities 
 by consumers are far more important than several 
 
116 STATISTICS IN BUSINESS 
 
 times this number which enter only insignificantly into 
 living costs. The same consideration is equally true 
 in the construction of a wholesale series, a cost of pro- 
 duction series, and a securities series. 
 
 Moreover, the collection of prices and use of index 
 numbers are difficult in another way. There are 
 producers' and consumers' prices, jobbers' and mill 
 prices, wholesale and retail prices. There are prices 
 in large markets under conditions of world competi- 
 tion, and prices in isolated communities where mo- 
 nopoly essentially rules. The selection of prices raises 
 such questions as the following: 
 
 What is meant by price; is the price retail or whole- 
 sale; under what condition is price named; to what 
 grade of commodity or service does it apply; on what 
 market is it quoted; are "prices" contract, import or 
 freely competitive in character? 
 
 Now, there are various ways in which index numbers 
 may be computed. A simple form is illustrated on 
 pages 113-114. In this case, 1913 is taken as a base. 
 The prices are calculated as relatives or percentages 
 on this year and the percentages averaged. But 
 neither a base nor an average is necessary. Actual 
 prices may be reduced to a common denominator, as 
 so much per pound, and simply added together. 
 The result is a series of amounts in dollars and cents. 
 It is in this form in which Bradstreet's number is 
 calculated. Bradstreet's numbers for recent years 
 are given in Table 12. 
 
 The Annalist index number is different. It is a 
 weekly number made from the wholesale prices of 
 twenty-five commodities chosen in such a way as to 
 represent the principal items in a family budget. It 
 
SUMMARIZING THE PACTS 
 
 117 
 
 Table 12 — Table Giving BKADsTBEiT's Commodity Price Index 
 Numbers, Jantiart, 1903 to Joly, 1919 
 
 Year 
 
 Index number; first of the month 
 
 January 
 
 AprU 
 
 July 
 
 October 
 
 1903 
 
 S8.0789 
 
 7.9885 
 
 8.0827 
 
 8.3289 
 
 8.9172 
 
 8.2949 
 
 8.2631 
 
 9.2310 
 
 8.8361 
 
 8.9493 
 
 9.4935 
 
 8.8857 
 
 9.1431 
 
 10.9163 
 
 13.7277 
 
 17.9436 
 
 18.5348 
 
 88.1247 
 
 7.9690 
 
 7.9996 
 
 8.2987 
 
 8.9640 
 
 8.0650 
 
 8.3157 
 
 9.1996 
 
 8.5223 
 
 9.0978 
 
 9.2976 
 
 8.7562 
 
 9.7753 
 
 11.7598 
 
 14.5769 
 
 18.4431 
 
 17.2795 
 
 87.8706 
 
 7.6318 
 
 7.9160 
 
 8.2835 
 
 9.0409 
 
 7.8224 
 
 8.4573 
 
 8.9246 
 
 8.5935 
 
 9.1119 
 
 8.9521 
 
 8.6566 
 
 9.8698 
 
 11.5294 
 
 16.0680 
 
 19.1624 
 
 18.8964 
 
 87.9083 
 
 1904 
 
 7.9213 
 
 1905 
 
 8.2298 
 
 1906 
 
 8.5580 
 
 1907 
 
 8.8506 
 
 1908 
 
 8.0139 
 
 1909 
 
 8.7478 
 
 1910 
 
 8.9267 
 
 1911 
 
 8.8065 
 
 1912 
 
 9.4515 
 
 1913 
 
 9 . 1526 
 
 1914 
 
 9.2416 
 
 1915 
 
 9.9774 
 
 1916 
 
 12.0399 
 
 1917 
 
 16.9135 
 
 1918 
 
 18.9942 
 
 1919 
 
 19.5215 
 
 
 
 Table 13. — Table Giving the Annalist's Yearly Commodity 
 
 Price Index Numbers, 1890 to September, 1919 
 
 (Base period 1890 to 1899 = 100) 
 
 Year 
 
 Index 
 number 
 
 Year 
 
 Index 
 
 number 
 
 Year 
 
 Index 
 number 
 
 1890 
 
 1891 
 
 109.252 
 
 119.488 
 
 108.624 
 
 116.100 
 
 102.076 
 
 94.604 
 
 80.096 
 
 84.092 
 
 92.208 
 
 93.348 
 
 1900 
 
 1901 
 
 1902 
 
 1903 
 
 1904 
 
 1905 
 
 1906 
 
 1907 
 
 1908 
 
 1909 
 
 99.388 
 104.656 
 116.264 
 107.516 
 108.664 
 110.652 
 114.364 
 117.940 
 125.756 
 133.952 
 
 1910 
 
 137 . 172 
 
 1911 
 
 131 . 068 
 
 1892 
 
 1912 
 
 143.254 
 
 1893 
 
 1913 
 
 139.980 
 
 1894 
 
 1914 
 
 146.069 
 
 1895 
 
 1915 
 
 148.055 
 
 1896 
 
 1916 
 
 175.720 
 
 1897 
 
 1917 
 
 261.796 
 
 1898 
 
 1918 
 
 287.080 
 
 1899 
 
 1919 to Sept. 1 
 
 301.904 
 
118 
 
 STATISTICS IN BUSINESS 
 
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SUMMARIZING THE FACTS 119 
 
 is calculated as an average of relatives, as is the ex- 
 ample on pp. 113-114, but uses as a base the average 
 of the prices, 1890-1899. The yearly numbers for the 
 years since 1890 appear in Table 13. 
 
 In Table 14 a number of American and foreign 
 wholesale price index series have been reduced to a 
 common base by dividing the index in each series 
 for 1913, on the original base, into the index for each 
 year or month on that base. For some of the series 
 this process gives only approximately correct results, 
 but these are sufficiently accurate for general purpose 
 comparisons. 
 
 The most satisfactory index number of retail 
 prices for the measurement of the changing prices of 
 foods is that compiled by the United States Bureau 
 of Labor Statistics. This series is shown in the 
 following ratio chart for the years 1913-1919. 
 
 The principal peculiarities of index or relative 
 numbers of prices may be summarized as follows: 
 
 First. — " No index number corresponds 
 
 to a real thing An index number points to 
 
 no single fact. It gives only an indication 
 
 of a general trend. People often think and speak 
 loosely on this topic, as if an index number told the 
 whole story once for all. There is no one change in 
 prices. There is a medley of changes, different in 
 direction and degree. All that we can hope to secure 
 by averaging and summarizing is some concise state- 
 ment of the general drift." 
 
 Second. — Index numbers ot wholesale and retail 
 commodities should be distinguished. The conditions 
 under which wholesale and retail prices are deter- 
 
120 
 
 STATISTICS IN BUSINESS 
 
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SUMMARIZING THE FACTS 121 
 
 mined are different, as are also the uses to which they 
 should be put. 
 
 Third. — For any index number the types of the 
 commodities which are used are significant. Dis- 
 tinction should be made, for instance, in wholesale 
 index series, between producers' and consumers' 
 goods; between raw and manufactured commodities; 
 between mineral, animal, and farm products. All of 
 these respond differently to conditions of scarcity and 
 surplus, and time and place. 
 
 Fourth. — In using index numbers consideration 
 should be given to the number of commodities used, 
 the places from which quotations are taken, and the 
 frequency with which they are included. 
 
 Fifth. — Index numbers of prices should be con- 
 sidered from the point of view of the method by which 
 they are computed. In this respect the following are 
 important. 
 
 (o) Are the numbers average prices or actual prices? 
 If average prices, what average is used and with what 
 effect? 
 
 (6) Are the commodities taken as of equal impor- 
 tance, or are some commodities assigned greater 
 importance than others? 
 
 (c) If weights are assigned to indicate relative 
 importance, upon what basis are they chosen? 
 
 (d) If a base year is used, what, if any, significance 
 is there in the period chosen? 
 
 Sixth. — General purpose should not be confused 
 with special purpose index numbers of prices. 
 
 Other phases of index numbers of prices are impor- 
 tant to the business executive, but they cannot be 
 treated here. For a fuller discussion of them, the 
 
122 STATISTICS IN BUSINESS 
 
 reader may consult the author's Introduction to 
 Statistical Methods. 
 
 Now, what are some of the inconsistencies of which 
 the business man and others are guilty in the use of 
 price index summaries? There are many, but only a 
 few will be suggested here. 
 
 First. — The demand for wage increase is brought 
 to a head in a strike, and justification is sought by 
 labor in the increased cost of living. The business 
 man consults a price index series, but unfortunately, 
 he chooses the wrong one. It may be Bradstreet's, 
 or the Bureau of Labor Wholesale series to which he 
 refers, and from which he develops his argument. 
 He is in error, (a), in choosing a wholesale series; 
 (6), in construing the change of prices as indicated 
 as equivalent to cost of living changes; (c), in choosing 
 a general purpose series and using it for a particular 
 use; (d), in failing to see that the weights assigned to 
 commodities have nothing to do with the scale in 
 which the commodities enter into consumers' budgets. 
 
 Second. — Need arises for some measure of the whole- 
 sale prices of manufactured producers' goods, such, for 
 instance, as farm or other machinery. The Annalist 
 index number is used, notwithstanding the fact that 
 68 per cent, of the manufactured commodities con- 
 tained in this number are consumers' rather than 
 producers' goods, and that 32 per cent, of the com- 
 modities are, in fact, raw rather than manufactured 
 materials. 
 
 Third. — Similarly, an index number is wanted which 
 will serve as a general barometer of business, and 
 Dun's is chosen, notwithstanding the fact that it is 
 given as the amount in dollars and cents which is 
 
SUMMARIZING THE FACTS 123 
 
 required to purchase a year's supply of goods for an 
 individual at a given time, and is not as susceptible 
 to market changes in prices as is Bradstreet's or the 
 Bureau of Labor's wholesale number. 
 
 It is unnecessary to give further examples of the 
 unscientific use of summarized price data. The above 
 illustrations undoubtedly, are of daily occurrence. 
 Here, fact analysis is ignored, and the scientific 
 method has no place. 
 
 Business facts must be summarized and digested, 
 and averages are useful in the process, whether applied 
 to prices, wages, costs, sales, or what not. The 
 process of summarization, however, is fundamental, 
 and the spirit in which it is done, exacting. The 
 technique is important here as it is in tabulation and 
 graphics, and it is hoped that what has been said will 
 at least serve the purpose of emphasizing the scientific 
 attitude in which the technique should be applied, 
 and of describing briefly the ways in which detail 
 may be summarized. 
 
CHAPTER VII 
 
 COMPARISON AND THE ESTABLISHMENT OF 
 BUSINESS PRINCIPLES AND STANDARDS 
 
 The modern business executive must see business 
 facts and relations in their larger aspects. Business 
 is intensely human. It deals in the last instance 
 with individuals and with groups, and the psychology 
 of both must be understood. Moreover, the fact 
 must be appreciated that the time, place, and condi- 
 tion under which business is carried on, are vital in 
 the comparisons which are made, the standards w^hich 
 are set up, and the principles which are established. 
 Business is controlled by customary and statutory 
 law, as well as by its legal interpretation. The in- 
 stitutions of property, custom, and contract also 
 affect business at every turn, and its plans must be 
 interpreted in the light of them. Similarly, political 
 ideals are potent in shaping the sphere which business 
 assumes, and in controlling its development. Compe- 
 tition is also an important factor and the exercise of 
 personal initiative important. These larger facts and 
 relationships cannot be ignored. 
 
 Just how these larger aspects of business are signi- 
 ficant must be determined upon an analysis of each 
 type of enterprise, and the nature of its immediate 
 problems. Custom may control in the determination 
 of the prices of goods and services, and in the wages 
 which are paid. Statutory law may control the 
 
 124 
 
BUSINESS PRINCIPLES AND STANDARDS 125 
 
 form of business and the expenses under which it 
 operates. In the latter aspect, taxes and other pay- 
 ments imposed by governments are instances in point. 
 Concerning them, business must take an enlightened 
 and positive attitude and provide for them in the 
 accounts which are kept and the plans which are 
 made. Of these facts, business, of course, is fully a^are 
 in a general way when problems arise, but it does not 
 always see their full import from day to day and 
 make provision for them. 
 
 The point which is being stressed is that business 
 must be considered in' its relative aspects, and that 
 those who are in control must not be unmindful of its 
 relationship to the underlying forces of economic, 
 pohtical, and social life. It is necessary, of course, 
 to see one's individual problems, and to settle them 
 with regard to the effect which the solution will have 
 on profits, on public approval, and on the interests 
 of those who are instrumental in bringing success. 
 But for a business executive solely to see them as his 
 problems, and to treat them as if they were unrelated 
 to the larger political, economic, and social currents 
 of the times, is, of course, to lose sight of the factors 
 which at bottom make them problems at all. If this 
 is done, the solutions offered may be temporary and 
 bring with them later more serious and fundamental 
 problems, the solution of which lies outside of the ken 
 and the experience of the individual estabUshment. 
 Tampering with the labor 'problem — putting off facing 
 the real problems by refusing to meet the real issues, 
 or by ignoring that they exist — for instance, is a case 
 in point. This problem is far larger than any estab- 
 lishment, and its issues more fundamental than those 
 
126 STATISTICS IN BUSINESS 
 
 which are the subject of controversy within a given 
 industrial concern. How this problem, Uke others, is 
 related to group psychology, to poUtical and social 
 ideas, and how it may be constructively met, must be 
 determined by business if it is to function smoothly 
 and the cooperation upon which it rests is to endure. 
 
 Although the problems of business are relative to 
 time, place, and condition, and are intimately related 
 to such institutions as custom, property, and con- 
 tract, and to problems of psychology, many of them 
 may be stated in definite terms and the facts which 
 define and measure them be determined. What these 
 facts are, the conditions which must be established in 
 order to measure them, and the ways in which they 
 may be summarized have been suggested in the pre- 
 ceding pages. What must now be emphasized are the 
 conditions which make comparisons and the establish- 
 ment of standards and principles valid for business 
 uses. How are the results of the appUcation of sci- 
 entific methods to business to be realized and made 
 to contribute to business success? 
 
 The establishment of business standards and princi- 
 ples results from comparison. For things to be com- 
 pared, they must possess points in common, and to 
 determine common quaUties, uniform standards of 
 measurements must be applied. A business fact, 
 however, is not a uniform thing; it does not always 
 exhibit itself in the same way. It cannot always be 
 treated uniformly and subjected to one foot-rule. It 
 is complex and varied and requires that the units of 
 measurements applied to it shall be adjusted according 
 to the form in which it reveals itself. Hence, com- 
 parisons of business facts are never perfect; they are 
 
BUSINESS PRINCIPLES AND STANDARDS 127 
 
 experimental and approximate. The standards must 
 constantly be changed and adapted to time, place, 
 and condition. Because of change in circumstances, 
 what is true today, under a given condition, may not 
 be true tomorrow. 
 
 If comparisons are difficult to make and are often 
 misleading, then the establishment of cause and effect 
 relations in a narrow and absolute sense is virtually 
 impossible. It is a tempting thing for a business 
 executive to reason, that if A happens, B will result. 
 He would like to be sure, for instance, that if prices 
 are lowered, sales will be stimulated; that if he puts 
 more money into advertising, larger sales will be 
 experienced; that if he grants the increase of wages 
 demanded, labor will be satisfied. Unfortunately, 
 peace of mind does not come in this way; a quantita- 
 tive cause does not necessarily bring with it an equal 
 quantitative effect. The result is not absolute, but 
 relative. Business does not go on repeating itself in 
 a round of sameness, nor do the effects of certain 
 causes always remain identical. Variation is always 
 present. 
 
 To illustrate, stimulation of business is shown in 
 increased bank clearings and in expanding loans, but 
 not all banks are equally affected, nor is business 
 uniformly speeded up. Surplus reserves of banks 
 are related to interest rates on call loans, but will an 
 X reserve always give a Y rate? A change in whole- 
 sale prices causes the retail prices to fluctuate, but 
 will a change of 20 per cent., for instance, in the whole- 
 sale price of hides always bring 20 per cent, change in 
 the price of shoes? To ask such questions is to 
 answer them; and yet, is it not customary in business 
 
128 STATISTICS IN BUSINESS 
 
 for plans to be made and policies pursued as if there 
 were, underlying the whole business structure, some 
 automatic and perfectly certain cause and effect 
 machinery? 
 
 Business phenomena are related; they do stand in 
 the relationship of cause and effect to each other, but 
 this is not so simple and so predictable as it is some- 
 times indicated to be. What the relationship is can 
 rarely if ever be guessed; but it can be measured, and 
 it is the function of scientific method to determine it. 
 
 There is a Science of Business. The method by 
 which it is discovered and stated is the same as that 
 which is employed in the natural sciences; but the 
 difficulties of applying it are vastly more serious. 
 Experimentation is not so easy; the factors which are 
 dealt with are far more complex, and the conditions 
 under which they operate more diverse and difficult of 
 standardization. But the problem of understanding 
 it is not insuperable. The absolutely indispensable 
 conditions upon which it rests are first, a whole- 
 some respect and an unconditional demand for the 
 truth; second, scientific observation and measure- 
 ment of business facts; third, the application of facts 
 to business problems upon the basis of working hypo- 
 theses, with the purpose of determining their relative 
 truths; and fourth, the formulation of standards and 
 principles as rules for business guidance. 
 
 A. business synthesis is sadly needed, not alone of 
 the activities of individual business establishments, 
 but of industries as well. Such a synthesis hes within 
 the power of every concern and of industries too, the 
 moment that it is seriously wanted. Fact analysis 
 supplies the method. What is most needed is a 
 
BUSINESS PRINCIPLES AND STANDARDS 129 
 
 disposition seriously to employ it on the requisite scale. 
 Business rivalry and diminished profits require that 
 business be scientific, and the new competition sug- 
 gests the ways in which savings and economies may be 
 introduced. What is needed among competitors 
 is common statistical activity and exchange of informa- 
 tion. More analysis of business facts and equal 
 sharing in the results are necessary. The old dogma, 
 "the gain of one is the loss of another," needs to be 
 abandoned. Bureaus of research, or research depart- 
 ments, must become a component part of every 
 business establishment, and the scientific method the 
 point of view of every business executive. 
 
 What the scientific method is has been fully de- 
 scribed. What the facts of business are which should 
 be analyzed have been suggested, and the ways indica- 
 ted in which complex data may be summarized. Hav- 
 ing caught the spirit of fact analysis, and understanding 
 what it implies, it is the indispensable function of an 
 executive to apply it to his problems. Moreover, 
 it is essential for employers' organizations, business 
 clubs, and managers' associations, to study scientific 
 method in relation to business problems and to install 
 machinery whereby the experiences of all may be put 
 at the service of each. 
 
 When businesses have done this, either individually 
 or cooperatively, industry will be seen in a new light. 
 The principles and rules for guidance then will not 
 be formulated out of prejudice nor arrived at in an 
 occult or rule-of-thumb manner, but will be established 
 on the basis of facts scientifically analyzed and prop- 
 erly interpreted. They will not be accepted blindly, 
 but with discrimination, and the conditions will be 
 
130 STATISTICS IN BUSINESS 
 
 established for making business scientific. Fact 
 analysis will become the rule, and industry will prosper 
 as a result of its application. The standards of fact 
 analysis are severe, its methods are exact, but the 
 results worth while. Business must be conducted on 
 a scientific basis. 
 
 There are, therefore, in summary, two phases to 
 scientific method, as applied to business or other 
 phenomena: first, scientific observation, and second, 
 logical inference. In the application of these stand- 
 ards, a science of business is to be developed. 
 
INDEX 
 
 Accidents, 16; compensation for, 16; how measured statistically, 28; 
 statistics of, and comparability, 28. 
 
 Accounting and Statistics, 3. 
 
 Accuracy, meaning and standards of, 34-35. 
 
 Advertising and custom, 36. 
 
 Analysis, business, requirements of, 3-4, 10, 12; relation of comparison 
 to, 30. 
 
 Annalist's index number, 112; 1890 to 1919, 117; how calculated, 
 116-117, 119; peculiarities of, 122. 
 
 Average, average measure the best measure, 103; the arithmetic 
 mean, 100-104; (arithmetic mean), characteristics of, 101, 104; 
 (arithmetic mean), how computed, 101; relationship of (arith- 
 metic mean) to the mode, 109; concept of, 97-99; the median 
 (see Median) ; the mode (see Mode). 
 
 Averages, as summaries of details, 123; choice of, for business analysis, 
 109-110; relation of, to business problems, 99-100, 102; sampling 
 and, 102-104; use of, to summarize prices, 111-112. 
 
 B 
 
 Babson service, 22-23. 
 
 Bank clearings, as measure of trade buoyancy, 29. 
 
 Banking, 21. 
 
 Bar-diagrams, com.ponent parts and (illustrated), 73; order of detail 
 
 and (illustrated), 72, 73, 74. 
 Bars, component parts and (illustrated), 74, 79, 80, 81; constrasted 
 
 with surfaces (illustrated), 75, 78; cross-hatching in (illustrated), 
 
 79; position of, 62; use of, as contrasted with lines connecting 
 
 bars in historical series, 86-88; use of, for comparisons of size, 61; 
 
 use of subdivided, for presenting component parts, 62; use of 
 
 vertical, in frequency distributions, 62. 
 Base lines in diagrams, 59. 
 Bias, 31. 
 Bradstreet's index nimiber, 112; how calculated, 116; 1903 to 1919, 
 
 117; peculiarities of, 122. 
 
 131 
 
132 INDEX 
 
 Brinton, W. C, Graphic Methods for Presenting Facts, 58. 
 
 Brookmire Service, 22-23. 
 
 Buildings, 23. 
 
 Bureau of Labor price index number, 112. 
 
 Business, a "going" concern, 36; cause and effect relations in, 127-128; 
 competition and, 2; facts of, classified, 5; meaning of, 1; modern, 
 contrasted with ancient, 2; seen by different interests, 1-2; seen 
 through averages, 99-100; the science of, 128; uses of index 
 numbers in, 115-116. 
 
 Business advertising and custom, 36. 
 
 Business analysis, cooperatively undertaken, 129-130; misuse of 
 index numbers in, 122-123; questions which it will answer, 36-37 
 scientific method and, 38-40; scientific method in, 129-130 
 scope of, 125-126; short- and long-time influences and, 34 
 standards and, 128; steps in, 128; use of averages in, 109-110 
 use of tables in, 54; what it requires, 3-4, 8, 10, 12. 
 
 Business barometer, Bradstreet's index number a, 123. 
 
 Business, cooperative, 12; custom and, 124^125; law and, 124-125; 
 poUtical ideals and, 124-125; property relations and, 124^125. 
 
 Business facts, capital, 8-9; character of, 27; classified, 13; commen- 
 surable, 26; credit, 9-10; depreciation rate, 11-12; frequency of 
 measurement of, 34; investments, 9; labor, 8; land, 11; land, 
 classified, 14; law and policy, 14; market, 7; market, classified, 14; 
 meaning and use of, 29; production, 6; production, classified, 13; 
 profits, 10, 11; sales, 7; taxes, 11; transportation, classified, 14. 
 
 Business judgments, crude data and, 30; facts and, 2; general, and 
 ■ statistical facts, 29. 
 
 Business operations, the measurement of facts and, 36. 
 
 Business policy, shaped through analysis, 37-38. 
 
 Business problems, relative aspects of, 126. 
 
 Business research, 36 
 
 Business records, custom and, 36. 
 
 Business standards, statistical analysis and, 37. 
 
 Business synthesis, how realized, 128-129. 
 
 Capital facts, 8-9, 18-19; classified, 13; earnings, 18-19; resources, 18. 
 
 CapitaUzation vs. capital, 18. 
 
 Cause and effect, business relations in the order of, 128. 
 
 Census, 20. 
 
 Circle diagrams to represent component parts (illustrated), 65-67. 
 
 Classification, relation to tabulation, 41. 
 
INDEX 133 
 
 Classification of facts, 41 ; meaning of, 41-42. 
 
 Collection of data, schedules and, 51 ; relation of, to tabulation, 51. 
 
 Color diagrams, 61. 
 
 Comparison, essence of, 126-127; what it involves, 30. 
 
 Comparison in business analysis, 126-127. 
 
 Competition, business analysis and, 37. 
 
 Component parts, choice of graphics for expressing, 61-62. 
 
 Cooperation in business, 12. 
 
 Cost facts, 12. 
 
 Cost of living, sampling and, 32; choice of index numbers to measure, 
 
 115-116; measurement of, 32. 
 Costs, business analysis and, 36; meaning of average, 99-100. 
 Credit, 21. 
 
 Credit facts, 9-10, 14. 
 Crops, 19. 
 
 Cross-hatching, for presenting component parts, 62. 
 Curves, historical, 57-58; scales for, 57; smoothing of, 57; use of, 57, 
 
 D 
 
 Depreciation, rate of, 11-12. 
 
 Diagrams, arrangement of items and, 60; base lines in, 59; form of, and 
 
 the person for whom designed, 64; position of titles in, 60-61; 
 
 rules for general make up of, 59-61; scale units and, 59; size of 
 
 sheets and, 61; surfaces within surfaces and (illustrated), 76-77; 
 
 to include the data represented, 59; use of colors and, 61. 
 Dot Map, frequency (illustrated), 86; use of frequency, 83; varying 
 
 shades of dots in, 85; (illustrated), 88; varying size dots in, 84; 
 
 (illustrated), 87. 
 Dun's index number, 112; peculiarities of, 122-123. 
 
 E 
 
 Earnings, 15, 18-19. 
 
 Editing of schedules, 52-53. 
 
 Executive, attitude of, toward problems, 27. 
 
 Exports, as measure of trade buoyancy, 29. 
 
 Fact analysis, meaning, 3-4, 10, 12. 
 
 Facts of business, characteristics of, 5; classified, 5. 
 
 Failures, 22. 
 
 Forecasting, 22-23. 
 
134 INDEX 
 
 G 
 
 Graphic forms, choice of, 61-64; use of, for comparisons of size, 61; 
 use of, for comparison of component parts, 61-62; use of, in 
 frequency distributions, 62; use of, in presenting geographic 
 variations, 62-63; for presenting time variations, 63-64. 
 
 Graphics, 55-96; application of, to business analysis, 58; contrasted 
 with tabulation, 55; position of titles on graphs, 60-61; principles 
 covering use of, 56; rules for selection of, 55-56; use of bars in, for 
 comparisons of size, 61 ; use of lines in, for comparisons of size, 61. 
 
 Graphs, form of, and the person for whom designed, 64; historical, 
 67-58, 63; historical, use of straight lines in, 63; historical, and 
 vertical zero, 64; position of scales in historical, 64; rules for 
 general make up of, 59-61; scales for, 57; size of, and sheet, 61; 
 smoothing of, 57; use of, 57. 
 
 H 
 
 Harvard Committee on Economic Research, 23. 
 Hollerith tabulating machines, 53. 
 
 Income tax, returns, 49. 
 
 Immigration, 17-18. 
 
 Imports, as measure of trade buoyancy, 29. 
 
 Index number, Annalist's, 112; Bradstreet's, 112; Bureau of Labor, 
 112; Dun's, 112. 
 
 Index numbers, calculation of, 116; certain American and foreign, 
 compared, 118; defined, 112; method of calculation of, illustrated, 
 112-114; misuse of, in business, 122-123; points to be considered 
 in use of, 115-116; principles governing construction and use of, 
 119-121. 
 
 Index number of food prices, graph of, 120. 
 
 Investment facts, 9, 14. 
 
 Labor facts, 8; accidents, 16; classified, 13, 15-18; compensation for 
 accidents, 16; immigration, 17-18; strikes and lockouts, 16; 
 turn-over, 17; unemployment, 16-17; union membership, 15-16; 
 wage-rates and earnings, 15. 
 
 Labor turn-over, comparability of statistics on, 28. 
 
INDEX 135 
 
 Land facts, 11, 23; classified, 14. 
 
 Law and Policy facts, 14, 24-25. 
 
 Lines, use of, for comparisons of size, 61. 
 
 Logarithmic charts, scale units and, 59; (see "Ratio" chart). 
 
 M 
 
 Maps, use of, 56; use of dot, 62; use of shaded, 63. 
 
 Market, conditions affecting, 30-31; how to measure the, 30-31. 
 
 Market analysis by sampling, 31-32. 
 
 Market extension through business analysis, 36-37. 
 
 Market facts, 7, 21-23; classified, 14; banking, 21; commodity prices, 
 22; credit, 21; failures, 22; forecasting, 22-23; land and building, 
 23; money, 21; security prices, 22; trade, 21-22. 
 
 Median, characteristics of the, 104-107; relation of the, to the arith- 
 metic mean, 106; how to calculate the, 107. 
 
 Mode, characteristics of the, 108-109; defined, 107; relationship of the, 
 to the median, 109; to the arithmetic mean, 109; use of the, in 
 business analysb, 109. 
 
 Money, facts of, 21. 
 
 Moody service, 22-23. 
 
 O 
 
 Occupations, accuracy of data on, 35. 
 OflSce records, use of, 36. 
 
 Pie-diagrams, to represent component parts (illustrated), 65-67. 
 
 Population, distribution of, 20-21. 
 
 Population facts, 13, 20-21; classified, 12. 
 
 Powers tabulating machines, 54. 
 
 Price index number, Annalist's, 112; Bradstreet's, 112; Bureau of 
 Labor, 112; Dun's, 112. 
 
 Price indexes and special use, 112. 
 
 Prices, commodity, 22; meaning of. 111, 116; methods and problems of 
 measurement of, 111-123; security, 22; uses of summaries of, 
 111-112. 
 
 Production facts, 6, 19-20; classified, 13; costs, 12; crops, 19; manufac- 
 tures, 20; raw materials, 19-20. 
 
 Production records, use of, 36. 
 
 Profits, facts on, 10, 11; meaning of average, 99-100; measurement ofi 
 34. 
 
136 INDEX 
 
 Q 
 
 Quartiles, meaning of the, 105. 
 
 Questionnaires, editing of, 52-53; principlee in preparing, 51-52. 
 
 R 
 
 "Ratio" chart (illustrated), 93; characteristics of the, 94-96. 
 ' Ratio" charts, contrast of, with difference charts, 92-96. 
 Raw materials, mineral, 19-20. 
 Research and business, 36. 
 
 S 
 
 Sales campaigns, population characteristics in developing, 30. 
 
 Sales facts, 7. 
 
 Sales records, use of, 36. 
 
 Salesmen, reports of, 37. 
 
 Salesmanship, standards of, 37. 
 
 Sampling, "law of averages" and, 102-104; principles of, 31-32. 
 
 Samples, requirements of good, 103. 
 
 Scale, horizontal, in graphics, 57; logarithmic, to measure ratio 
 
 changes, 64; vertical, in graphics, 57; vertical, in logarithmic 
 
 charts, 64; figures, 59; units, and logarithmic charts, 59; position 
 
 of, in frequency distributions, 62. 
 Scales, spacings on vertical and horizontal (illustrated), 68; use of, in 
 
 graphs (illustrated), 69. 
 Scientific method, business analysis and, 38-40; classification and, 
 
 50; fact analysis and, 36; meaning of, 3-4, 8, 12; phases of, in 
 
 business analysis, 129-130. 
 Schedules, editing of, 52-53; principles in making, 51-52. 
 Secondary sources, use of data from, 54. 
 
 Secrist, Horace, An Introduction to Statistical Methods, 58, 122. 
 Selling costs, business analysis and, 36. 
 Standardization, meaning of, in business statistics, 29. 
 Statistical facts, must be accurate, 34-35; must be comparable, 34; 
 
 must fit, 33; must be homogeneous, 30-31 ; must be representative, 
 
 31-33; must be stable, 33-34. 
 Stock prices, measurement of, 33. 
 
 Strike, how measured statistically, 28; as a statistical fact, 27-28. 
 Surfaces and bars contrasted (illustrated), 75, 
 
INDEX 137 
 
 T 
 
 Tables, preparation of useless, in business operations, 54. 
 
 Tabulation, advantages of, 41-42; a means not and end, 54; business 
 analysis through, 60; condensed detail and, 48; contrasted with 
 graphics, 55; grouping in, 49; hand and machine, 53-54; order 
 of detail in, 43-46; position of totals in, 46; principles to be fol- 
 lowed in, 43-48; relation of, to the collection of data, 51, 53; 
 relation of, to classification, 41, 53; titles to tables and, 47-48; 
 unclassified material and, 50. 
 
 Tax facts, 11, 14. 
 
 Trade facts, 21-22. 
 
 Transportation facts, 23-24; classified, 14. 
 
 Turn-over, meaning of average, 100; of goods, comparison of, 31; 
 of labor, 17; of labor, comparisons of, 31. 
 
 Unemployment, 16-17. 
 Union membership, 15-16. 
 
 U 
 
 W 
 
 Wage, meaning of average, 99. 
 
 Wage-rates, 15. 
 
 Wages, accuracy of, 35. 
 
 Wholesale prices, measurement of, 32-33. 
 
 Z 
 
 Zero hne, marking of (illustrated), 69-70; vertical scale and, 86-88.