## 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*.