In statistics, the arithmetic mean, or just the mean or average is the central tendency of a group of numbers taken as the sum of the numbers and then divided by the size of that group. The group is mostly the sample space of an experiment. The term “arithmetic mean” is used in mathematics and statistics to differentiate it from other means such as the harmonic and geometric mean.

The arithmetic mean is used commonly in fields such as economics, history, and sociology. This term is used in almost all the academic fields in some or other context. For example, per capita GDP gives an estimate of the arithmetic average income of the nation’s population.

**Definition**

Let us assume a sample space . The arithmetic mean is now defined as

If the list consists of a statistical population, then mean of that population is referred as a population mean and if the list includes a statistical sample, then the resulting statistic is a sample mean.

The arithmetic mean of a variable is generally denoted by a bar, for example

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