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 % |

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