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.
