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Probability and Statistics (view source)
Revision as of 14:59, January 19, 2009
, 14:59, January 19, 2009New page: {{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 = \operat...
{{math-h}}
'''Variance''' is a measure in [[Statistics|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 - \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.
[[category:Probability and Statistics]]
[[Category:Mathematics]]
'''Variance''' is a measure in [[Statistics|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 - \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.
[[category:Probability and Statistics]]
[[Category:Mathematics]]