Question

Mean deviation of the observations 70, 42, 63,34, 44, 54, 55, 46, 38, 48 from median is

• A. $7.8$
• B. $8.6$
• C. $7.6$
• D. $8.8$

Answer 1

The correct option is B $8.6$

Arranging the given data in ascending order-

$34,38,42,44,46,48,54,55,63,70$

$\because n=10$

Therefore,

Median $\left(M\right)=\frac{{\left(\frac{n}{2}\right)}^{th}\text{term}+{(\frac{n}{2}+1)}^{th}\text{term}}{2}$

$\Rightarrow M=\frac{46+48}{2}=47$

Therefore,

$x_i$	$|x_i-M|$
$34$	13
$38$	9
$42$	5
$44$	3
$46$	1
$48$	1
$54$	7
$55$	8
$63$	16
$70$	23
	$\sum |x_i-M|=86$

Therefore,

Mean deviation $=\frac{\sum |x_i-M|}{n}=\frac{86}{10}=8.6$

Hence the mean deviation of the observations is $8.6$.