Variance:Probability and Statistics - Revision history

DavidB4-bot: /* top */clean up & uniformity

2016-07-13T21:19:27Z

top: clean up & uniformity

RJJensen at 21:12, November 8, 2009

2009-11-08T21:12:14Z

Qwestor at 15:32, January 19, 2009

2009-01-19T15:32:03Z

Qwestor: New page: {{math-h}} '''Variance''' is a measure in statistics of the dispersion of a set of values (represented as $X$ ). It is defined as : $\sigma^2 = \operat...$

2009-01-19T15:06:59Z

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...

New page

{{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]]

← Older revision		Revision as of 21:12, November 8, 2009
Line 19:		Line 19:

	[[category:Probability and Statistics]]		[[category:Probability and Statistics]]
−	~~[[Category:Mathematics]]~~

@@ Line 1: / Line 1: @@
 {{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
+'''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>
@@ Line 18: / Line 18: @@
-[[category:Probability and Statistics]]
+[[Category:Probability and Statistics]]

@@ Line 10: / Line 10: @@
 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>
+:<math>S_{n}^2 =  {\sum_n(X_n - \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.

Variance:Probability and Statistics - Revision history

DavidB4-bot: /* top */clean up & uniformity

RJJensen at 21:12, November 8, 2009

Qwestor at 15:32, January 19, 2009

Qwestor: New page: {{math-h}} '''Variance''' is a measure in statistics of the dispersion of a set of values (represented as X). It is defined as :\sigma^2 = \operat...

Qwestor: New page: {{math-h}} '''Variance''' is a measure in statistics of the dispersion of a set of values (represented as $X$ ). It is defined as : $\sigma^2 = \operat...$