# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# Variance

Variance[list]
gives the sample variance of the elements in list.

Variance[dist]
gives the variance of the symbolic distribution dist.

## DetailsDetails

• Variance measures dispersion of data or distributions.
• Variance[list] gives the unbiased estimate of variance.
• Variance[list] is equivalent to Total[(list-Mean[list])^2]/(Length[list]-1) for real-valued data.
• For complex data, Variance[list] is equivalent to (list-Mean[list]).Conjugate[list-Mean[list]]/(Length[list]-1).
• Variance handles both numerical and symbolic data.
• Variance[{{x1,y1,},{x2,y2,},}] gives {Variance[{x1,x2,}],Variance[{y1,y2,}]}.
• Variance[dist] is equivalent to Expectation[(x-μ)2,xdist] with μ=Mean[dist].

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

Variance of a list of numbers:

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Variance of elements in each column:

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Variance of a symbolic lognormal distribution:

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