## Moment Coefficient of Kurtosis for ungrouped data

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

Moment coeff. of kurtosis
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 Kurtosis :($\beta_2$)
Coeff. of Kurtosis :($\gamma_2$)

## Moment Coefficient of Kurtosis for ungrouped data

The moment coefficient of kurtosis is denoted as $\beta_2$ and is defined as $$\begin{equation} \beta_2=\frac{m_4}{m^2_2} \end{equation}$$

The gamma coefficient of kurtosis is defined as $$\begin{equation} \gamma_2 = \beta_2 - 3 \end{equation}$$

• If $\gamma_2 >0$ or $\beta_2 > 3$, then the frequency distribution is leptokurtic.
• If $\gamma_2 =0$ or $\beta_2 = 3$, then the frequency distribution is mesokurtic.
• If $\gamma_2 <0$ or $\beta_2 < 3$, then the frequency distribution is platykurtic.