Editing Arithmetic mean (section)

{{Short description|Type of average of a collection of numbers}}
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{{broader|Mean}}
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In [[mathematics]] and [[statistics]], the '''arithmetic mean''' ({{IPAc-en|pron|ˌ|æ|r|ɪ|θ|ˈ|m|ɛ|t|ɪ|k|audio=LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-arithmetic.wav}} {{respell|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.<ref>{{cite book|last=Jacobs|first=Harold R.|title=Mathematics: A Human Endeavor|edition=Third|year=1994|publisher=[[W. H. Freeman]]|page=547|isbn=0-7167-2426-X}}</ref> The collection is often a set of results from an [[experiment]], an [[observational study]], or a [[Survey (statistics)|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 mean|geometric]] and [[harmonic mean|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 tendency|central tendencies]], it is not a [[robust statistic]]: it is greatly influenced by [[outlier]]s (values much larger or smaller than most others). For [[skewed distribution]]s, 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.