## Mean Absolute Deviation for grouped data

Use this calculator to find the Mean Absolute Deviation for grouped (raw) data.

Mean Absolute Deviation Calculator | |
---|---|

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): | |

Sample Mean : ($\overline{x}$) | |

Mean Absolute Deviation : (MAD) | |

## Mean Absolute Deviation

Let `$x_i, i=1,2, \cdots , n$`

be $n$ observations
then the mean of $X$ is denoted by $\overline{x}$ and is given by
```
$$
\begin{aligned}
\overline{x}& =\frac{1}{N}\sum_{i=1}^{n}f_ix_i.
\end{aligned}
$$
```

where $N = \sum_{i=1}{n} f_i$.

The mean absolute deviation about mean is denoted by MAD and is given by
```
$$
\begin{aligned}
MAD & =\frac{1}{N}\sum_{i=1}^{n}f_i|x_i -\overline{x}|
\end{aligned}
$$
```