Definition:Arithmetic 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:


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

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.


 * Definition:Mean


 * Definition:Arithmetic-Geometric Mean
 * Definition:Geometric Mean
 * Definition:Harmonic Mean
 * Definition:Hölder Mean
 * Definition:Weighted Mean


 * Cauchy's Mean Theorem
 * Arithmetic Mean is Never Less than Harmonic Mean
 * Definition:Average Value of Function

Other measures of central tendency that are often introduced in schools at the same time:


 * Definition:Mode
 * Definition:Median (Statistics)