# Probability and Statistics

 $\frac{d}{dx} \sin x=?\,$ This article/section deals with mathematical concepts appropriate for a student in late high school or early university.

Variance is a measure in statistics of the dispersion of a set of values (represented as X). It is defined as

$\sigma^2 = \operatorname{E}[(X-\operatorname{E}[X])^2] = \operatorname{E}[X^2] - (\operatorname{E}[X])^2$

where the expected value of X is E(X).

The formula for variance must not be confused with the formula

$S_{n}^2 = {\sum_n(x - \bar x)^2 \over n - 1}$

which is the formula for a point estimate of the true variance from a sample of size n. As such this estimator itself has a variance which, as the formula indicates, decreases as the sample size increases.