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In case of average of weighted relatives, price relative of each commodity is multiplied by the weight of that commodity and the sum of these products is divided by the sum of weights of all the commodities. Weighted average-of-relatives index can be calculated by taking arithmetic mean as well as geometric mean as average. If arithmetic mean is taken as average then formula will be:

Geometric mean is sometimes used as an average. The weighted average-of-relatives (G.M.) is computed by the formula

Problem: For the data given below in the table, construct weighted average of relative’s index using; (a) Arithmetic mean as the average (b) Geometric mean as the average while taking 1993 as base.

Solution:

### Arithmetic mean as the average

The Weighted average-of-relatives index is calculated by taking mean as average. This calculation is shown in the table given below.

### Geometric mean as the average

Since Weighted average-of-relatives index is calculated by taking geometric mean as average therefore the formula of geometric mean will be used. The calculation is shown in the table given below.

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