Sample variance
sample dispersion
A scalar characteristic of the disperson, or spread, of a sample (consisting of real numbers) relative to a fixed point (called the centre of dispersion). It is numerically equal to the sum of the squares of the deviations of the values from
. For real-valued random variables
, the variable
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is the sample variance about . The variables
are often assumed to be independent and identically distributed in discussions about
. Since, for any
,
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where , the sample variance about
will be minimal when
. A small value of
indicates a concentration of the sample elements about
and, conversely, a large value of
indicates a large scattering of the sample elements. The concept of a sample variance extends to that of a sample covariance matrix for multivariate samples.
References
[1] | S.S. Wilks, "Mathematical statistics" , Wiley (1962) |
Sample variance. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sample_variance&oldid=18175