Question

Find mean deviation from median for the given data.

$x$	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
$f$	$5$	$8$	$15$	$16$	$6$

• A. $8.28$
• B. $9.56$
• C. $10.19$
• D. $13.65$

Answer 1

The correct option is B $9.56$

$\text{Class}$	$f_i$	Class frequency$\left(cf\right)$	Mid-Value$\left(x_i\right)$	$|x_i-\text{Median}|$	$f_i|x_i-\text{Median}|$
$0-10$	$5$	$5$	$5$	$23$	$115$
$10-20$	$8$	$13$	$15$	$13$	$104$
$20-30$	$15$	$28$	$25$	$3$	$45$
$30-40$	$16$	$44$	$35$	$7$	$112$
$40-50$	$6$	$50$	$45$	$17$	$102$

$N=\sum f_i=50$

Here, $N=50$, so $\frac{50}{2}=25$ and the cummulative frequency is just greater than $\frac{N}{2}$ is $28$.

Thus, $20-30$ is median class.

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

$F$ $=$ Cummulative frequency before median class $=13$

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

Frequency of median class $=$ $f=15$

Median $=l+\frac{\frac{N}{2}-F}{f}\times h=20+\frac{25-13}{15}\times 10=28$

$\sum f_i\times |x_i-\text{Median}|=478$

Mean deviation about the mean $=\frac{1}{N}\sum f_I\times |x_i-\text{Median}|=\frac{1}{50}\times 478=9.56$