## Moment Coefficient of Kurtosis for grouped data

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

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

## Moment Coefficient of Kurtosis for grouped 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.