# Weighted Arithmetic Mean

You have studied various methods of computing arithmetic mean for different types of data sets. In all these methods we presume that all the items of the given data set have equal importance. But it is not necessarily true in all situations. In practical situations some items are of greater importance  than the others. For example, while constructing the cost of living index for a particular class, the commodities they consume have varying importance. The simple arithmetic mean of the prices of such commodities will not depict a true picture of their living pattern. Different commodities are to be assigned weights and a weighted arithmetic mean is to be worked out in such situations. In a factory where unit cost of manufacturing is to be worked out, a weighted average is more appropriate. Thus the term weight refers the relative importance of the different items.

Uses of Weighted Arithmetic Mean

Weighted arithmetic mean is mainly useful under the following situations:

1) When the given items are of unequal importance

2) When averaging percentages which have been computed by taking different number of items in the denominators

3) When statistical measures such as mean of several groups are to be combined To be more specific, weighted arithmetic mean is used in the following cases:

1) Construction of Index Numbers.

2) Computation of standardised birth and death rates.

3) Finding out an average output per machine, where machines are of varying capacities.

4) Determining the average wages of skilled, semi-skilled and unskilled workers of a factory.