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: \(\overline{\textrm{x}}\).
Some books prefer the notation \(\overline{\textrm{X}}\). - 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 \(x_1, x_2, x_2, x_3, x_4, …, x_n\), then the arithmetic mean of E is given by:
\(\overline{\textrm{x}} = \dfrac{x_1 + x_2 + x_2 + x_3 + x_4 + … + x_n}{n}\)
Examples
Consider the numbers: 3, 5, 7, 9, 11, 13.
The arithmetic mean of these numbers is: \(\overline{\textrm{x}}\) = \(\frac{3\space +\space 5\space +\space 7\space +\space 9\space +\space 11\space +\space 13}{6}\) = 8.