is known as a "weighted" average. If, reversely, beef is "weighted" twice as much as wheat, the average rise is and the index number is 108. It will be noted that there is remarkably little difference between the "weighted" averages on the one hand (106 and 108), and the "unweighted" average (107) on the other. Such is usually the case. Figure 1 illustrates this important fact. Nor does it generally make
Fig. 1. Price Movements as Calculated by Different Methods
(after Wesley Clair Mitchell)
Showing how very closely the "weighted" and "unweighted" methods of averaging agree with each other. That is, the percentage by which the level of wholesale prices in the United States has changed between any two dates is found to be about the same whether that percentage is calculated "unweighted," i.e. as a simple average of the percentages by which the various commodities have changed in price, all of them being treated alike, or "weighted," i.e. with careful regard to the relative importance of each commodity. Thus, between 1896 and 1914 the "weighted" index number rose from 67 to 100, and the "unweighted" from 90 to 133. The two rises are almost identical, 100⁄67 being almost the same as 133⁄90.
(The curves in this, and the other, diagrams in this book are plotted on the "ratio chart" in which the vertical scale is so arranged that the same slope always represents the same percentage rise.)
much difference whether very many or only a moderate number of commodities are included. Figure 2 illustrates this fact.
On the whole, the best form of index number is that expressing the price of a given bill of goods. If a defi-
