# Arithmetic Mean

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Definition

Arithmetic MeanGiven - [math]\overline{x} = \frac{x_1 + x_2 + ... + x_n}{n}.[/math]
The arithmetic mean can also be written: - [math]\overline{x} = \frac{1}{n}\sum_{i=1}^n x_i.[/math]
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:

- [math]12,10,13,14,16,18,17\,[/math]

The arithmetic mean is the sum of these numbers, **[math]100[/math]**, divided by the total number of entries in the list, **[math]7[/math]**, equal to **[math]14.285[/math]**

- [math]\overline{x} = \frac{12+10+13+14+16+18+17}{7}=\frac{100}{7}=14.285\,\![/math]

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