Question

Find mean deviation about median

Class	$2-4$	$4-6$	$6-8$	$8-10$
Frequency	$3$	$4$	$2$	$1$

• A. $1.4$
• B. $2.4$
• C. $5.23$
• D. $7.78$

Answer 1

The correct option is A $1.4$

$\text{Class}$	$f_i$	Cummulative Frequency$\left(cf\right)$	Mid-Value$x_i$	$|x_i-\text{Median}|$	$f_i|x_i-\text{Median}|$
$2-4$	$3$	$3$	$3$	$2$	$6$
$4-6$	$4$	$7$	$5$	$0$	$0$
$6-8$	$2$	$9$	$7$	$2$	$4$
$8-10$	$1$	$10$	$9$	$4$	$4$

$N=\sum f_i=10$

Here, $N=10$ , so $\frac{10}{2}=5$ and the cummulative frquency is just greater than $\frac{N}{2}$ is $7$.

Thus, $4-6$ is median class.

$l$ $=$ lower limit of median class $=4$

$F$ $=$ Cummulative frequency before median class $=3$

Difference between the class $=$ $h=2$

Frequency of median class $=$ $f=4$

Median $=l+\frac{\frac{N}{2}-F}{f}\times h=4+\frac{5-3}{4}\times 2=5$

$\sum f_i\times |x_i-\text{Median}|=14$

Mean deviation about the median $=\frac{1}{N}\sum f_I\times |x_i-\text{Median}|=\frac{1}{10}\times 14=1.4$