## 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 $$$$\beta_1 = \frac{m^2_3}{m^3_2}$$$$ where $m_2$ and $m_3$ are second and third central moments.

The gamma coefficient of skewness is defined as $$$$\gamma_1 = \sqrt{\beta_1}= \frac{m_3}{m^{3/2}_2}$$$$

• 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.