# 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.

### Notation

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 $$\overline{x}_p$$.

### Example

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 %

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