## 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*.