Difference between revisions of "Variance:Probability and Statistics"
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| − | '''Variance''' is a measure in [[ | + | '''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> | :<math>\sigma^2 = \operatorname{E}[(X-\operatorname{E}[X])^2] = \operatorname{E}[X^2] - (\operatorname{E}[X])^2</math> | ||
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| − | [[ | + | [[Category:Probability and Statistics]] |
Latest revision as of 21:19, July 13, 2016
| <math>\frac{d}{dx} \sin x=?\,</math> | This article/section deals with mathematical concepts appropriate for late high school or early college. |
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_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.