Moment Coefficient of Skewness for grouped data
Use this calculator to find the Coefficient of Skewness based on moments for grouped data.
| Moment coeff. of Skewness | |
|---|---|
| Type of Freq. Dist. | DiscreteContinuous |
| Enter the Classes for X (Separated by comma,) | |
| Enter the frequencies (f) (Separated by comma,) | |
| Results | |
| Number of Obs. (n): | |
| Mean of X values: | |
| First Central Moment :($\mu_1$) | |
| Second Central Moment :($\mu_2$) | |
| Third Central Moment :($\mu_3$) | |
| Fourth Central Moment :($\mu_4$) | |
| Coeff. of Skewness :($\beta_1$) | |
| Coeff. of Skewness :($\gamma_1$) | |
Moment Coefficient of Skewness for grouped data
Moment Coefficient of Skewness is denoted by $\beta_1$ and is
defined as
$$ \begin{equation} \beta_1 = \frac{m^2_3}{m^3_2} \end{equation} $$
where $m_2$ and $m_3$ are second and third central moments.
The gamma coefficient of skewness is defined as
$$ \begin{equation} \gamma_1 = \sqrt{\beta_1}= \frac{m_3}{m^{3/2}_2} \end{equation} $$
- If $\gamma_1 >0$ or $\mu_3 > 0$, then the data is positively skewed.
- If $\gamma_1 =0$ or $\mu_3 = 0$, then the data is not skewed (symmetric).
- If $\gamma_1 <0$ or $\mu_3 < 0$, then the data is negatively skewed.
