Question

Find the mean deviation from the mean of the following data:

$x_1$: 2 5 6 8 10 12
$f_1$: 2 8 10 7 8 5

Answer 1

$x$	$f$	$xf$	$|d\overline{x}|=|x-\overline{x}|$	$f|d\overline{x}|$
$2$	$2$	$4$	$5.5$	$11$
$5$	$8$	$40$	$2.5$	$20$
$6$	$10$	$60$	$1.5$	$15$
$8$	$7$	$56$	$0.5$	$3.5$
$10$	$8$	$80$	$2.5$	$20$
$12$	$5$	$60$	$4.5$	$22.5$
	$\sum f=40$	$\sum xf=300$		$\sum f|d\overline{x}|=92$

$\Rightarrow$ $Mean\left(\overline{x}\right)=\frac{\sum xf}{\sum f}=\frac{300}{40}=7.5$

$\Rightarrow$ Mean deviation from mean $=\frac{\sum f|d\overline{x}|}{\sum f}$

$=\frac{92}{40}$

$=2.3$