## Central moments for ungrouped data

Let $x_1,x_2,\cdots, x_n$ be $n$ observations. The mean of $X$ is denoted by $\overline{x}$ and is given by $$\begin{eqnarray*} \overline{x}& =\frac{1}{n}\sum_{i=1}^{n}x_i \end{eqnarray*}$$

## Formula

The first four central moments are as follows

### $m_4 =\frac{1}{n}\sum_{i=1}^n (x_i-\overline{x})^4$

where,

• $n$ total number of observations
• $\overline{x}$ sample mean