Moment coefficient of kurtosis for grouped data
Let $(x_i,f_i), i=1,2, \cdots , n$ be given frequency distribution. The mean of $X$ is denoted by $\overline{x}$ and is given by
$$ \begin{eqnarray*} \overline{x}& =\frac{1}{N}\sum_{i=1}^{n}f_ix_i \end{eqnarray*} $$
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
$N=\sum_i f_i$total number of observations$\overline{x}$sample mean$m_2 =\frac{1}{N}\sum_{i=1}^n f_i(x_i-\overline{x})^2$is second central moment$m_4 =\frac{1}{N}\sum_{i=1}^n f_i(x_i-\overline{x})^4$is fourth central moment
