## 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