Difference between revisions of "Probability and Statistics"
Jump to navigation
Jump to search
(New 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...) |
DavidB4-bot (talk | contribs) (→top: clean up & uniformity) |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
{{math-h}} | {{math-h}} | ||
| − | '''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> | ||
| Line 16: | Line 16: | ||
| − | [[ | + | [[Category:Probability and Statistics]] |
| − | |||
Latest revision as of 17:52, 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 - \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.