# Definition:Arithmetic Mean

This page is about Arithmetic Mean in the context of Algebra. For other uses, see Mean.

## 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:

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

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

## Also known as

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, or just mean value or mean.

## Also see

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

• Results about arithmetic mean can be found here.

## Linguistic Note

In the context of an arithmetic mean, the word arithmetic is pronounced with the stress on the first and third syllables: a-rith-me-tic, rather than on the second syllable: a-rith-me-tic.

This is because the word is being used in its adjectival form.