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''sample dispersion''

A scalar characteristic of the disperson, or spread, of a sample (consisting of real numbers) relative to a fixed point  $  x $(
called the centre of dispersion). It is numerically equal to the sum of the squares of the deviations of the values from  $  x $. 
For real-valued random variables  $  X _ {1} \dots X _ {n} $, 
the variable

$$ 
S _ {n} ( x)  = \ 
\sum _ {i = 1 } ^ { n } 
( X _ {i} - x)  ^ {2}
$$

is the sample variance about  $  x $. 
The variables  $  X _ {1} \dots X _ {n} $
are often assumed to be independent and identically distributed in discussions about  $  S _ {n} ( x) $. 
Since, for any  $  x $,

$$ 
S _ {n} ( x)  =  S _ {n} ( \overline{X}\; ) + n ( \overline{X}\; - x)  ^ {2}  \geq  \ 
S _ {n} ( \overline{X}\; )  \equiv  S _ {n} ,
$$

where  $  \overline{X}\; = ( X _ {1} + \dots + X _ {n} )/n $, 
the sample variance about  $  x $
will be minimal when  $  x= \overline{X}\; $. 
A small value of  $  S _ {n} $
indicates a concentration of the sample elements about  $  \overline{X}\; $
and, conversely, a large value of  $  S _ {n} $
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====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  S.S. Wilks,   "Mathematical statistics" , Wiley  (1962)</TD></TR></table>