Second central momentum = μ2

Synonym: Second central momentum (μ₂) = Variance

The 2^nd order central momentum, 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 $\begin{array}{l}\mu(x)\end{array}$ :

$\begin{array}{l}\displaystyle \mu_2 = E[ ( x - \mu)^2 ] = \frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2\end{array}$

where

$\begin{array}{l}N\end{array}$	dataset length
$\begin{array}{l}E\end{array}$	estimating operator

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.

Page tree

Second central momentum = μ2