Question

Calculate Mean deviation about median for the given data

Marks	$100-110$	$110-120$	$120-130$	$130-140$	$140-150$
Frequency	$4$	$6$	$5$	$3$	$2$

• A. $10.5$
• B. $31.5$
• C. $12.5$
• D. $66.16$

Answer 1

The correct option is A $10.5$

$\text{Class Interval}$	$f_i$	Cummalative frequency$\left(cf\right)$	$\text{Mid-Value}\left(x_i\right)$	$|x_i-\text{Medain|}$	$f_i|x_i-\text{Median}|$
$100-110$	$4$	$4$	$105$	$15$	$60$
$110-120$	$6$	$10$	$115$	$5$	$30$
$120-130$	$5$	$15$	$125$	$5$	$25$
$130-140$	$3$	$18$	$135$	$15$	$45$
$140-150$	$2$	$20$	$145$	$25$	$50$
	$N=20$				$\sum f_I|x_i-\text{Median}|=210$

Median class$=$ value of $(\frac{n}{2}{)}^{th}$ obsrevation $=$ vaue of ${10}^{th}$ observation $=$ class $(120-130)$

Median class will be $120-130$

$L$ $=$ Lower boundary point of median class $=$ $120$

$n$ $=$ Total frequency $=$ $20$

$F$ $=$ Cummulative frequency of class before median class $=$ $115$

$f$ $=$ Frequency of the median class $=$ $5$

$h$ $=$ class length of median class $=$ $10$

Median $=$ $L+\frac{\frac{n}{2}-F}{f}\times h=120+\frac{10-10}{5}\times 10=120$

Mean deviation $\frac{\sum f_i|x_i-\text{Median}|}{n}=\frac{210}{20}=10.5$