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# arithmetic mean

The arithmetic mean of a set of values is determined by dividing the sum of the values by the number (count) of the values. For example, the average of the numbers 9, 14, and 31 is given by

$\displaystyle\frac{9+14+31}{3}=18.$

More generally, if $$x_1,x_2,\ldots,x_n$$ are a set of values, then the arithmetic mean, denoted $$\overline{x}$$, is given by

$\overline{x} = \displaystyle\frac{1}{n} \sum_{i=1}^n x_i.$

In statistics the mean is one measure of central tendency of a dataset, but it is sensitive to asymmetry and outliers in the data.

Citation Info

• [MLA] “arithmetic mean.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 18 Feb 2014. Web. 18 Feb 2014. <http://platonicrealms.com/>
• [APA] arithmetic mean (18 Feb 2014). Retrieved 18 Feb 2014 from the Platonic Realms Interactive Mathematics Encyclopedia: http://platonicrealms.com/encyclopedia/arithmetic-mean/