Empirical Standard Deviation

statistics

Definition

Empirical Standard Deviation

Given a random sample $X_1,X_2,\dots ,X_n$ from the distribution of the random variable $X$ with realisation $x_1,x_2,\dots ,x_n$.

The empirical standard deviation is given by

$$\begin{array}{rl}& \\ S& =\sqrt{\frac{\left({\sum }_i^n(X_i-\bar{X}{)}^2\right)}{n-1}}\\ s& =\sqrt{\frac{\left({\sum }_i^n(x_i-\bar{x}{)}^2\right)}{n-1}}\end{array}$$