Talk:Algorithms for calculating variance: Difference between revisions

Revision as of 18:55, 25 December 2010

Revision as of 19:28, 25 December 2010

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Can somebody explain why there are two different flavors of the formula for variance, one where you divide by n, the other where you divide by n-1? Obviously, for large values of n, they approach each other, but why the difference at all? -- [[User:RoySmith|RoySmith]] [[User Talk:RoySmith|(talk)]] 18:55, 25 December 2010 (UTC)

: Wikipedia's mathematics reference desk would probably be a better place for this sort of question.

: Notice that

:* The rule that

::: var(''X'' + ''Y'') = var(''X'') + var(''Y'')

:: when ''X'' and ''Y'' are [[independence (probability theory)|independent]] [[random variable]]s applies when you divide by ''n'' and '''not''' when you divide by ''n'' − 1.

:* Dividing by ''n'' − 1 is done when one is trying to [[estimation (statistics)|estimate]] the variance of a population by using a random sample. It should never be done when one has the whole population and the variance can be computed exactly. It's effect is to make the estimate [[bias (statistics)|unbiased]]. That's not really all that good a reason to do it, but that's why it's done. See [[Bessel's correction]] for an account of some of the mathematical theory.

:* This is standard textbook material. Maybe more of it should be included in the article.

: [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 19:28, 25 December 2010 (UTC)