Calculate the mean deviation about the mean for the following frequency distribution:

Class interval	$0-4$	$4-8$	$8-12$	$12-16$	$16-20$
Frequency	$4$	$6$	$8$	$5$	$2$

First,find the mid-points $(x_i)$ for each class interval and calculate the mean $(\bar{x})$:

Class interval	$f_i$	$x_i$	$f_i x_i$	$|x_i - \bar{x}|$	$f_i |x_i - \bar{x}|$
$0-4$	$4$	$2$	$8$	$|2 - 9.2| = 7.2$	$28.8$
$4-8$	$6$	$6$	$36$	$|6 - 9.2| = 3.2$	$19.2$
$8-12$	$8$	$10$	$80$	$|10 - 9.2| = 0.8$	$6.4$
$12-16$	$5$	$14$	$70$	$|14 - 9.2| = 4.8$	$24.0$
$16-20$	$2$	$18$	$36$	$|18 - 9.2| = 8.8$	$17.6$
Total	$\Sigma f_i = 25$		$\Sigma f_i x_i = 230$		$\Sigma f_i d_i = 96$

$\bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} = \frac{230}{25} = 9.2$
$\text{Mean deviation} = \frac{\Sigma f_i |x_i - \bar{x}|}{\Sigma f_i} = \frac{96}{25} = 3.84$