View source for Variance:Probability and Statistics

{{math-h}}

'''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 [[expectation (math)|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_n - \bar X)^2 \over n - 1}</math>

(where <math>\bar X =  {\sum_n X_n  \over N}</math> is the [[sample mean]]).

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.



[[Category:Probability and Statistics]]