# Probability and Statistics

From Conservapedia

<math>\frac{d}{dx} \sin x=?\,</math> | 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 <math>X</math>). It is defined as

- <math>\sigma^2 = \operatorname{E}[(X-\operatorname{E}[X])^2] = \operatorname{E}[X^2] - (\operatorname{E}[X])^2</math>

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

The formula for variance must not be confused with the formula

- <math>S_{n}^2 = {\sum_n(x - \bar x)^2 \over n - 1}</math>

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.