Question

Find the mean derivation from the mean for the following data

$x_1$	$2$	$5$	$6$	$8$	$10$	$12$
$y_1$	$2$	$8$	$10$	$7$	$8$	$5$

Answer 1

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

$\Rightarrow$ $Mean\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{\sum f_i}$

$=\frac{300}{40}$

$=7.5$

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

$=\frac{92}{40}$

$=2.3$