## Moment Coefficient of Skewness for ungrouped data

Use this calculator to find the Coefficient of Skewness based on moments for ungrouped (raw) data.

Moment coeff. of Skewness
Enter the X Values (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 ungrouped 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.