Problem Of Weighted Arithmetic Mean
Suppose the incomes of two groups of persons are as follows :—
The average income of each of these two groups is $ 300. It would appear from the averages that both the groups are economically at the same level, and the two series are almost similar to each other but this is not the case. The two series entirely differ from each other, so far as their composition is concerned
The arithmetic average gives greater importance to higher items of a series and lesser importance to smaller items. It has an upward bias. One big item among four items, three of which are small, will push up the average consi-
The formula can be written in short as :—
Xw = ∑Xw / ∑w
Where ∑XW stands for the sum of the products of the values and their respective weights, and ∑ w for the sum of the weights .
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