## Moment coefficient of kurtosis 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 moment coefficient of kurtosis $\beta_2$ is defined as

`$\beta_2=\dfrac{m_4}{m_2^2}$`

The moment coefficient of kurtosis $\gamma_2$ is defined as

`$\gamma_2=\beta_2-3$`

where

`$n$`

total number of observations`$\overline{x}$`

sample mean`$m_2 =\frac{1}{n}\sum_{i=1}^n (x_i-\overline{x})^2$`

is second central moment`$m_4 =\frac{1}{n}\sum_{i=1}^n (x_i-\overline{x})^4$`

is fourth central moment