# Arithmetic Mean

< MathGloss‎ | A

This glossary is far from complete. We are constantly adding math terms.
For instructions on adding new terms, please refer to Math Glossary Main Page


Definition
 Arithmetic Mean Given n numbers in any order, the arithmetic mean is defined as the sum of these n numbers divided by n. If the n observations are x1, x2, ..., xn, their mean, which we denote by $\overline{x}$ (and read X-bar), is therefore: $\overline{x} = \frac{x_1 + x_2 + ... + x_n}{n}.$ The arithmetic mean can also be written: $\overline{x} = \frac{1}{n}\sum_{i=1}^n x_i.$ When the term "mean" is used without the modifier "arithmetic," it is assumed to refer to the arithmetic mean.

## Examples

Suppose we have a list of the following numbers:

$12,10,13,14,16,18,17\,$

The arithmetic mean is the sum of these numbers, $100$, divided by the total number of entries in the list, $7$, equal to $14.285$

$\overline{x} = \frac{12+10+13+14+16+18+17}{7}=\frac{100}{7}=14.285\,\!$