Question

Find the mean deviation about the mean for data.

$x_i$	5	10	15	20	25
$f_i$	7	4	6	3	5

Answer 1

$x_i$	$f_i$	$f_i{x}_i$	$|x_i-\overline{x}|$	$f_i|x_i-\overline{x}|$
$5$	$7$	$35$	$9$	$63$
$10$	$4$	$40$	$4$	$16$
$15$	$6$	$90$	$1$	$6$
$20$	$3$	$60$	$6$	$18$
$25$	$5$	$125$	$11$	$55$
	$\sum f_i=25$	$\sum f_i{x}_i=350$		$\sum f_i|x_i-\overline{x}|=131$

$\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{350}{25}=14$

$\Rightarrow$ Mean deviation about mean $=\frac{\sum f_i|x_i-\overline{x}|}{\sum f_i}$

$=\frac{131}{25}$

$=5.24$