## 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