Central momentum = μn

@wikipedia

A set of statistical metrics, characterizing the deviation of a given numerical dataset $\begin{array}{l}x = \{ x_1, \, x_2, \, x_3 , ... x_N \}\end{array}$ from its Mean Value $\begin{array}{l}\mu(x)\end{array}$ :

$\begin{array}{l}\displaystyle \mu_n = E[ ( x - \mu)^n ] = \frac{1}{N} \sum_{i=1}^N (x_i - \mu)^n\end{array}$

where

$\begin{array}{l}N\end{array}$	dataset length
$\begin{array}{l}E\end{array}$	expectation operator
$\begin{array}{l}n\end{array}$	order of central momentum

The common assumption is that zero-th central momentum is unit-value: $\begin{array}{l}\mu_0 \equiv 1\end{array}$ .

By definition the first central momentum is always zero: $\begin{array}{l}\mu_1 \equiv 0\end{array}$ .

The second central momentum (μ₂) is also called variance $\begin{array}{l}\mu_2 = \sigma^2\end{array}$ , where $\begin{array}{l}\sigma\end{array}$ is standard deviation.

The third central momentum is characterizing asymmetry of the dataset distribution $\begin{array}{l}\mu_3 = \bar \mu_3 \cdot \sigma^3\end{array}$ , where $\begin{array}{l}\bar \mu_3\end{array}$ is skewness.

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Central momentum = μn