Arithmetic Mean

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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 [math]\overline{x}[/math] (and read X-bar), is therefore:

[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.


Suppose we have a list of the following numbers:


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]