What is "arithmetic mean"

n. (context statistics probability English) The measure of central tendency of a set of values computed by dividing the sum of the values by their number; commonly called the '''mean''' or the '''average'''.

n. the sum of the values of a random variable divided by the number of values [syn: first moment, expectation, expected value]

In mathematics and statistics, the arithmetic mean , or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection. The collection is often a set of results of an experiment, or a set of results from a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps distinguish it from other means, such as the geometric mean and the harmonic mean.

In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, and it is used in 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, meaning that it is greatly influenced by outliers (values that are very much larger or smaller than most of the values). Notably, for skewed distributions, such as the distribution of income for which a few people's incomes are substantially greater than most people's, the arithmetic mean may not accord with one's notion of "middle", and robust statistics, such as the median, may be a better description of central tendency.

In a more obscure usage, any sequence of values that form an arithmetic sequence between two numbers x and y can be called "arithmetic means between x and y."