Method of Averaging Relatives

When there is a single commodity, the price index is simply the ratio of its current price to its base price, in percentage terms — the price relative, $\frac{P_1}{P_0}\times100$. With many commodities this method averages the price relatives.

Simple (unweighted) average of relatives:

where $n$ is the number of commodities. For the four goods:

a 49 per cent rise.

Weighted average of relatives — the weighted arithmetic mean of the price relatives:

Here weights $W$ are usually the share of each item in total expenditure in the base period (its value share); base-period weights are preferred to current ones because recomputing weights every year is inconvenient. With the following data:

a 56 per cent rise. The weighted index exceeds the unweighted one here because the most important item, A, doubled in price. …