The unadjusted sample variance measures the average dispersion of a sample of observations around their mean. It is computed by averaging the squared deviations from the mean.
It is also often called biased sample variance, because, under standard assumptions, it is a biased estimator of the population variance.
It is defined as follows:
Definition
Given
observations
![[eq1]](/images/unadjusted-sample-variance__2.png)
,
their unadjusted sample variance
is:![[eq2]](/images/unadjusted-sample-variance__3.png)
where
is their sample
mean:![[eq3]](/images/unadjusted-sample-variance__5.png)
The lecture entitled Variance estimation provides a thorough introduction to the concept of unadjusted sample variance, including a detailed analysis of its statistical properties (e.g. biasedness as an estimator of the population variance).
The glossary entry entitled Adjusted sample variance provides a short definition of another - unbiased - estimator of variance.
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