LIST OF PLATES 1. Value of Petroleum and Natural Gas, by States, 1909 (Illustrations of Lines, Surfaces, and Volumes) PAGE 165 2. Public School Property in 1904 and 1914. (Solids Drawn out of Scale) 3. Payments, Account Bonded Debt and Interest, on County Bonds 167 168 6. Color or Race, Nativity, and Parentage, by Divisions of the United States, 1910 174 7. Proportion of Insane Enumerated January 1, to Adult Population, 1904 and 1910 175 (Surfaces within Surfaces and Lines) 8. Proportion of Males 10 to 13 Years of Age Engaged in Gainful Occupations, by States, 1910 181 (Cross-hatched Map) 9. Primary Markets for Wisconsin Cheese (American), 1911 185 10. Pig-iron Production, by States, 1909 187 11. Number of Swine on Farms and Ranges, April 15, 1910 . 189 12. Number of Real Estate Mortgages in Wisconsin, 1904, by Rates of Interest . (Frequency Distribution, Discrete Series) 13. Smoothed Frequency Distribution of Lengths of Ears of Corn (Frequency Distribution, Continuous Series) 14. Capital and Clearings of New York Clearing House Banks, 1902-1915 PAGE 210 214 224 (Method of Scale Conversion) 15. Capital and Clearings of New York Clearing House Banks, 1902-1915 226 (Method of Scale Conversion) 16. Diagrams Illustrating the Nature of the Arithmetic Mean when Items are Differently Weighted . 243 17. Cumulative Graphs Ogives - Constructed on "More Than" and "Less Than" Bases, Showing by Towns the Classified Prices of Oil. 18. Cumulative Graphs Historigrams Constructed on "Up to and Including" and "After and Including" Bases, Showing by Years Importations of Raw Cotton into the United States 19. Historigrams Showing the Distributions of Ratios of Assessed Values of Buildings to the Assessed Values of Lands upon which they Stand, New York City, 1914 20. Distribution of the Price Variations of 241 Commodities in 1913. (Percentages of Rise or Fall in Prices) 21. Distribution of 5578 Price Variations (Percentages of Rise or Fall over Prices of Pre 265 267 280 309 314 ceding Year) 22. Curves Showing, by the Range and the Decil Methods, the Dispersion of the Fluctuations in Relative Wholesale Prices of 145 Commodities, 1890-1910 . PAGE 386 23. Types of Frequency Distributions 24. Curves Showing, for 1907-1908, Classified Wage-rates of Female Menders in Woolen and Worsted Establishments 393 420 25. Curves Showing, for 1909–1910, Classified Wage-rates of Female Menders in Woolen and Worsted Establishments 421 26. Graphic Figures Illustrating Correlation by Means of 500 Pairs of Throws of Dice 439 27. Curves Showing Long-time or Secular Changes 450 (Note Circulation of Canadian Chartered Ranks, and 28. Curves Showing Short-time or Cyclic Changes (Note Circulation of Canadian Chartered Banks and 451 AN INTRODUCTION TO STATISTICAL METHODS CHAPTER I THE MEANING AND APPLICATION OF STATISTICS AND STATISTICAL METHODS I. INTRODUCTION THE necessity of basing economic and business judgments upon facts and of being able properly to collect and interpret them in connection with almost all of the different phases of economic activity is a sufficient general excuse for submitting a volume, the main purpose of which is a study of the principles governing the collection, analysis, and synthetic treatment of numerical data. More and more economic and business policies are being advocated after careful study of facts, and those affected by these policies are more and more frequently asking that they be given these same facts in a definite and understandable form. The tendency to base a case, to advocate a far-reaching change, to stand sponsor for a program or to agitate a reform, upon an appeal to natural rights, or to the innate goodness or perversity of human nature, is rapidly being overcome. Appeal to the force of custom and tradition alone no longer suffices as a basis for an economic program. If considered at all it is only to explain or appraise the facts involved. What is now being done is more closely to observe the reaction of forces under given |