Question

Calculate mean deviation about median for the given data

Class	$0-10$	$10-20$	$20-30$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$5$	$4$	$3$	$2$	$2$	$1$	$1$

• A. $2.3$
• B. $11.3$
• C. $12$
• D. $15$

Answer 1

The correct option is D $15$

$\text{Class}$	$f_i$	Cummulative Frequency$\left(cf\right)$	Mid-Value$\left(x_i\right)$	$|x_i-\text{Median}|$	$f_i|x_i-\text{Median}|$
$0-10$	$5$	$5$	$5$	$15$	$75$
$10-20$	$4$	$9$	$15$	$5$	$20$
$20-30$	$3$	$12$	$25$	$5$	$15$
$30-40$	$2$	$14$	$35$	$15$	$30$
$40-50$	$2$	$16$	$45$	$25$	$50$
$50-60$	$1$	$17$	$55$	$35$	$35$
$60-70$	$1$	$18$	$65$	$45$	$45$

$N=\sum f_i=18$

Here, $N=18$, so $\frac{18}{2}=9$ and the cummulative frequency is just greater than $\frac{N}{2}$ is $12$.

Thus, $20-30$ is median class.

$l$ $=$ lower limit of median class $=20$

$F$ $=$ Cummulative frequency before median class $=9$

Difference between the class $=$ $h=10$

Frequency of median class $=$ $f=3$

Median $=l+\frac{\frac{N}{2}-F}{f}\times h=20+\frac{9-9}{3}\times 10=20$

$\sum f_i\times |x_i-\text{Median}|=270$

Mean deviation about the mean $=\frac{1}{N}\sum f_I\times |x_i-\text{Median}|=\frac{1}{18}\times 270=15$