# Arithmetic mean

## Type of average of a collection of numbers / From Wikipedia, the free encyclopedia

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In mathematics and statistics, the **arithmetic mean** ( /ˌærɪθˈmɛtɪk ˈmiːn/ *arr-ith-MET-ik*), **arithmetic average**, or just the *mean* or *average* (when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection.^{[1]} The collection is often a set of results from an experiment, an observational study, or a survey. The term "arithmetic mean" is preferred in some mathematics and statistics contexts because it helps distinguish it from other types of means, such as geometric and harmonic.

In addition to mathematics and statistics, the arithmetic mean is frequently used in economics, anthropology, history, and almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.

While the arithmetic mean is often used to report central tendencies, it is not a robust statistic: it is greatly influenced by outliers (values much larger or smaller than most others). For skewed distributions, such as the distribution of income for which a few people's incomes are substantially higher than most people's, the arithmetic mean may not coincide with one's notion of "middle". In that case, robust statistics, such as the median, may provide a better description of central tendency.