Page:American Journal of Sociology Volume 6.djvu/120

 106 THE AMERICAN JOURNAL OF SOCIOLOGY

This typical brewer, who received over $6,000 per year, and was certainly worth that amount as a subject for statistical investigation, counted for as much in determining the simple average as 133 laborers included in a single series in establishment 48. The brewer's wages increased 275 per cent, between 1860 and 1891. The wages of the 133 laborers increased 29.5 per cent. The report has adopted a method of averaging that gives equal weight to each of these series, and figures out a simple average increase of 152.25 per cent, for the 134 workmen. In computing the weighted average for all industries the report makes a bad matter worse. The industry in which the brewer was employed is given a weight of 16, while that in which the 133 laborers were engaged receives a weight of 5. Such a method of weighing made the brewer simply invaluable for statistical purposes.

It may be noted also that in July, 1883, there appears on the pay- roll of this establishment a second brewer, at much lower wages than were paid to the first brewer, but that, instead of following the method adopted with other classes, viz., taking the average wages of these two employe's as representing brewers' wages, the report classifies the sec- ond brewer separately as an "assistant brewer." The assistant brewer's wages not making a complete series, they are omitted entirely from the computation. By this method the statistical value of the wages of the brewer was preserved.

Professor Mayo-Smith, in his recent work, Statistics and Economics, in discussing the use of index numbers of prices, shows the effect of giving undue weight to unimportant articles, saying :

Professor Falkner, for instance, has twenty-five quotations of pocket- knives out of a total of fifty-four for metals and implements, and a grand total of 223 articles. On the other hand he has but fifteen quotations for house-furnishing goods, of which seven are for wooden pails and tubs. He has but two quotations for vegetables (both potatoes) and four for fish (of which three are for salted mackerel). Undue prominence seems to be given to articles of no very great importance.

To show the effect upon the average of the food group of includ- ing the latter unimportant articles, this writer further remarks :

Among the articles which go to form the important index number for food are four kinds of fish. All of these show a rising price since 1860; and the single quotation of codfish gives an index number of 312 for 1891, on the basis of 100 for 1860. The whole index number for food shows a rise from 100 in 1860 to 103.9 m 1891. This is a very interesting fact, because food is a most important article of consumption, and this rise is in marked contrast with the fall of the great mass of commodities. If, however, we exclude the single item codfish, the number for 1891 becomes 99.9, and if we exclude all four quotations of fish which cover simply codfish and mackerel, the number