### Sample Variance

**Definition:**The

*sample variance*of a set of samples from a particular realization of a

*stationary stochastic process*is defined as

*average squared magnitude*after removing the

*known mean*:

(C.20) |

The sample variance is a

*unbiased estimator*of the true variance when the

*mean is known*,

*i.e.*,

(C.21) |

This is easy to show by taking the expected value:

When the mean is

*unknown*, the sample mean is used in its place:

(C.23) |

The normalization by instead of is necessary to make the sample variance be an

*unbiased*estimator of the true variance. This adjustment is necessary because the sample mean is

*correlated*with the term in the sample variance expression. This is revealed by replacing with in the calculation of (C.22).

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Cross-Correlation

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Variance