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 ¯x, we will note the weighted mean as ¯xp.
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 % |
¯xp=(72×15)+(65×20)+(78×30)+(70×35)15+20+30+35=71,7.