Empirical Variance

statistics

Definition

Empirical Variance

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 variance is given by

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