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Arithmetic Mean

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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\,\!




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