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Weighted Mean

The weighted mean is similar to the general mean, except that some points contribute more to the mean than some others. Mathematically if we have a set of points \(a_n\) and a set of weights \(w_n\) that belong to the points, then the weighted average is equal to

\( WAV=\sum_{i=1}^{n}\frac{a_iw_i}{w_i} = \frac{a_1w_1 + a_2w_2 + \cdots + a_nw_n}{w_1+w_2+\cdots+w_n} \)

for example, if we have two sets of points, 1 2 with weight 1 and 3 4 5 with weight 2, then the weighted average of all points is equal to

\( \frac{1 \times 1+2 \times1+3 \times2+ 4 \times2+5 \times2}{1+1+2+2+2}=\frac{1+2+6+8+10}{1+1+2+2+2}=\frac{27}{8}=3.375 \)

In excel there are two ways to calculate the weighted average. say we have the values in column A and the weights in column B.

In the first method we set the product of A and B in column C. Then, the weighted average is given by WAV = SUM(C:C)/SUM(B:B)

The second method uses the sumproduct function. This method doesn't require an additional column to be used. WAV = SUMPRODUCT(A:A,B:B)/SUM(B:B)

» WFM Glossary