Where the prices of a number of commodities increase or decrease during a given period, but at different rates, it is possible to indicate the general increase or decrease by the use of index numbers. If, for example, we find that:

2 bushels of commodity A sold for $1.00 in 1900 100 pounds of commodity B sold for $1.00 in 1900 5 yards of commodity C sold for $1.00 in 1900 and that 2 bushels of commodity A sold for $1.50 in 1910 100 pounds of commodity B sold for $1.30 in 1910 5 yards of commodity C sold for $1.25 in 1910 we may average the selling prices in 1900 and in 1910 and conclude that the prices of the three commodities considered together increased from $1.00 ([$1.00+$1.00+$1.00/3] =$1.00) to $1.35 ($1.50 + $1.30 + $1.25 = $1.35), or thirty-five per 3 cent. If, however, three times as many dollars' worth of A is sold as of either of the other commodities it will be necessary to "weight" the averages. This may be done by writing the price of A three times in the price columns and dividing by five instead of by three. The average for 1900 will still be one dollar but the average for 1910 will now be $1.50 + $1.50 + $1.50 + $1.30 + $1.25 = $1.41. We shall now say that as far as these three commodities are concerned prices have gone up forty-one per cent. If now, we should take a large number of representative commodities and calculate index numbers for prices in the various years we should be able to say whether, and how rapidly, prices as a whole were moving up or down. And since the prices of commodities and the value of money are reciprocals we should also be able to say how rapidly the value of money was decreasing or increasing. Thus, if the general level of prices increased from 100 to 141, or forty-one per cent in a given period, the value of money decreased from 100 to 100/141 (70.9) or 29.1 per cent.