Standardized central momentum = <μn>

@wikipedia

A set of statistical metrics, characterizing the average deviation of the numerical values in the given dataset $//<![CDATA[ \begin{array}{l}x = \{ x_1, \, x_2, \, x_3 , ... x_N \}\end{array} //]]>$ from its Mean Value  $//<![CDATA[ \begin{array}{l}\mu(x)\end{array} //]]>$ :

where 

The concept makes sense only for the central momentums of higher oder than  $//<![CDATA[ \begin{array}{l}n \geq 3\end{array} //]]>$, since lower order central momentums   $//<![CDATA[ \begin{array}{l}\bar \mu_0 \equiv 1/\sigma\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}\bar \mu_1 \equiv 0\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}\bar \mu_2 \equiv 1\end{array} //]]>$ are trivial and do not carry additional information on dataset distribution.

The most popular application is the 3-rd order standardized central momentum $//<![CDATA[ \begin{array}{l}\mu_3 = \bar \mu_3 \cdot \sigma^3\end{array} //]]>$, which is called skewness and characterizes asymmetry of the dataset distribution.

See also

Formal science / Mathematics / Statistics / Statistical Metric / Central momentum