The square root of the second central momentum \mu_2, characterizing the deviation of a given numerical dataset x = \{ x_1, \, x_2, \, x_3 , ... x_N \} from its Mean Value \mu(x) :
| \sigma(x) = \sqrt{\mu_2} = \sqrt{E[ ( x - \mu)^2 ]} = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2} |
where
It is often used as normalization denominator for higher order central momentums \mu_n: \bar \mu_n = \mu_n/\sigma^n, \ \ n \geq 3.
See also
Formal science / Mathematics / Statistics / Statistical Metric / Central momentum