## Mean absolute deviation for grouped data

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

be given frequency distribution. Then the sample mean is given by

```
$$
\begin{aligned}
\overline{x}&=\frac{1}{N}\sum_{i=1}^n f_ix_i.
\end{aligned}
$$
```

## Formula

The mean absolute deviation about mean for grouped data is given by

`$MAD =\frac{1}{N}\sum_{i=1}^{n}f_i|x_i -\overline{x}|$`

where,

`$N =\sum_{i=1}^n f_i$`

total number of observations`$\overline{x}$`

sample mean