Definition:Arithmetic Mean

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Definition

Let $x_1, x_2, \ldots, x_n \in \R$ be real numbers.

The arithmetic mean of $x_1, x_2, \ldots, x_n$ is defined as:

$\displaystyle A_n := \dfrac 1 n \sum_{k=1}^n x_k$

That is, to find out the arithmetic mean of a set of numbers, add them all up and divide by how many there are.

This is the quantity that is usually referred to in natural language as the "average" of a set of numbers. It is also known as the common mean.

Note that there are several kinds of average and indeed, several different kinds of mean. This is just one of them.

For the definition of the arithmetic mean of a real function, see Average Value of a Function.