Statistics

Arithmetic Mean

Quotient of the sum of the values in the distribution of a quantitative statistical characteristic by the number of values.

Notations

  • The arithmetic mean of a distribution is noted as: [latex]\overline{\textrm{x}}[/latex]. Some books prefer the notation [latex]\overline{\textrm{X}}[/latex].
  • When it is necessary to distinguish between the mean of an entire population and the mean of a sample, the mean of the entire population is generally noted as: μ.

Formula

If a distribution E includes the data [latex]x_1, x_2, x_2, x_3, x_4, ..., x_n[/latex], then the arithmetic mean of E is given by:

[latex]\overline{\textrm{x}} = \dfrac{x_1 + x_2 + x_2 + x_3 + x_4 + ... + x_n}{n}[/latex]

Examples

Consider the numbers: 3, 5, 7, 9, 11, 13. The arithmetic mean of these numbers is: [latex]\overline{\textrm{x}}[/latex] = [latex]\frac{3\space +\space 5\space +\space 7\space +\space 9\space +\space 11\space +\space 13}{6}[/latex] = 8.

See also:

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