Weighted Mean

Weighted Mean

If E is a set of numerical statistical data, P is a set of weights and R is a function of E in P that associates a weight to each value of E in P, then the weighted mean of the data in E is the quotient of the products of E × P by the sum of the weight.


Because a weighted mean is different from an arithmetic mean, it is sometimes helpful to use a different notation. So, for a distribution in which the arithmetic mean is \(\overline{x}\), we will note the weighted mean as \(\overline{x}_p\).


Consider a set of school grades described like this:

Steps Weights Notes
1 15 % 72 %
2 20 % 65 %
3 30 % 78 %
4 35 % 70 %
Total 100 % 71,7 %

\(\overline{x}_p = \dfrac {\left(72\times15\right)+\left(65\times20\right)+\left(78\times30\right)+\left(70\times35\right)} {15+20+30+35} = 71,7\).

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