In calculations involving simple arithmetic mean, all occurrences have exactly the same importance or weight. We then say that they have the same relative weight.

However, there are cases where occurrences have different relative importance. In these cases, the averaging shall take into account this relative importance or relative weight. This type of average is called arithmetic mean. **weighted**.

Pondering is synonymous with regret. In calculating the weighted average, we multiply each value of the set by its "weight", that is, its relative importance.

## Weighted arithmetic mean definition

The weighted arithmetic mean _{P} of a set of numbers x_{1}, x_{2}, x_{3},…, X_{no} whose relative importance ("weight") is respectively p_{1}, P_{2}, P_{3},… , P_{no} is calculated as follows:

_{P} =

That is, we add the products of the values by their weights and divide the result by the sum of the weights.

Example:

Alcebíades participated in a contest, where Portuguese, Mathematics, Biology and History tests were held. These tests had weight **3**, **3**, **2** and **2**respectively. Knowing that Alcebíades got 8.0 in Portuguese, 7.5 in Mathematics, 5.0 in Biology and 4.0 in History, what was the average he got?

_{P} =

Therefore, the average of Alcebíades was 6.45.

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