Arithmetic Mean

In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the central tendency of a collection of numbers taken as the sum of the numbers divided by the size of the collection. The collection is often the sample space of an experiment. The term "arithmetic mean" is preferred in mathematics and statistics because it helps distinguish it from other means such as the geometric and harmonic mean.

In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent. For example, per capita GDP gives an approximation of 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. Notably, for skewed distributions, 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.

Read more about Arithmetic Mean:  Definition, Motivating Properties, Problems, Angles

Famous quotes containing the word arithmetic:

    Under the dominion of an idea, which possesses the minds of multitudes, as civil freedom, or the religious sentiment, the power of persons are no longer subjects of calculation. A nation of men unanimously bent on freedom, or conquest, can easily confound the arithmetic of statists, and achieve extravagant actions, out of all proportion to their means; as, the Greeks, the Saracens, the Swiss, the Americans, and the French have done.
    Ralph Waldo Emerson (1803–1882)