Page:Stabilizing the dollar, Fisher, 1920.djvu/56

2 An index number is a number showing the average rise or fall of prices. Thus, if wheat has risen 4% since last month while beef has risen 10%, the average rise of wheat and beef is midway between 4% and 10%, or 7% (i.e. $$\frac{4+10}{2}=7$$). Then 107% is the "index number" for the prices of the two articles this month, on the basis of last month's prices taken as 100%. Or:

The same method applies, of course, to more than two prices. Thus, if three such prices rise respectively 4%, 4% and 10%, their average rise is $$\frac{4+4+10}{3}$$ or 6% and the "index number" is 106 as compared with the original price level of 100, taken as a base of comparison.

Such a calculation treats the commodities as equally important. If one commodity is more important than another, and we wish to be very particular, we may treat the more important commodity as the equivalent of two or three other commodities. Thus, suppose that wheat is twice as important as beef. If wheat rises 4% and beef 10% the average rise of the two together, instead of being $$\frac{4+10}{2}=7$$, as it would be if the commodities were regarded as equal, is $$\frac{4+4+10}{3}=6$$ just as though there were three commodities, thus making the index number 106 instead of 107. This