INDEX NUMBER, a statistical method of showing the changes in the value of money and of investigating and measuring variations in the prices of commoditie., in general or of a special group of the latter. An index number is the result of a combination of several items, each of which is a ratio between the price of a cer tain commodity at a particular time, and its price at another period which is taken as a standard. Such ratios are usually expressed as percentages. Thus the price of wheat in 1918 may according to a certain system be set down as 119, in comparison with its price from 1900 to 1910; that is the price of wheat in 1918 is to average price of wheat in the decade 1900-10 as 119:100. By some writers the term index num ber is applied to each item, as well as to the combination. Percentages are usually made by striking an average of them, but a result of equal generality is obtained from their sum. A good method of constructing an index number is to take a number of articles, say 25, compare the price of each at the current date with its price at the period taken as basis or standard and express the result as a percentage, placing the sum of these percentages as the index number. Such a process involves the following considera tions: what commodities are to be considered? How are prices to be ascertained? How are ratios between the prices of each at the current period and the basic period to be combined? These problems vary according to the purpose in view. A general plan is to include articles of consumption rather than materials or imple ments; retail prices should be used, not whole sale; general wages are butyments for personal services should be The proper combination of ratios is a weighted average. A general principle to be observed in assigning the weights is the importance of each to the consumer. A very extensive literature
has grown up concerning index numbers and the problems arising from them. Both the British Association for the Advancement of Science and the International Statistical In stitute have gone into the question thoroughly. The question at issue is what average should be used in combining the index numbers for the individual commodities. If the weighted arithe metic mean is used, the question is what weights are to be applied? Moreover, it is necessary to determine what commodities are to be included. The Economist table includes only 22, Sauerbeck 35, Falkner 223 and the United States Bureau of Labor 340. For these, in turn, various prices may be used (average prices or single quotations, wholesale or retail prices according to the plan followed), all of which again may depend on various sources such as trade journals, statements of merchants, government reports, etc. The standard year or standard period has also to be chosen. Mean index numbers may be utilized to determine other general tendencies besides the movement of prices. Thus the level of wages for large districts may be determined in this way, or the level of wages in a single great industry or special class of industries. The United States Bureau of Labor Statistics publishes an index number of wholesale prices and also indexes of retail prices. Consult 'Bulletin of the United States Bureau of Labor Statistics' whole No. 181 (October 1915, pp. 6, 10, 11, 257-263) ; Boyley, 'Elements of Statistics' . (London 1901) ; Layton, W. T., 'Introduction to the Study of Prices) (London 1912) ; Secrist, Horace, 'Introduction to Statistical Methods' (New York 1917) • Zizek, Franz, 'Statistical Averages' (New York 1913).