Moment coefficient of skewness 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 skewness $\beta_1$ is defined as
$\beta_1=\dfrac{m_3^2}{m_2^3}$
The moment coefficient of skewness $\gamma_1$ is defined as
$\gamma_1=\sqrt{\beta_1}=\dfrac{m_3}{m_2^{3/2}}$
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$m_3 =\frac{1}{N}\sum_{i=1}^n f_i(x_i-\overline{x})^3$is third central moment
