Question

Following is the distribution of I.Q. of $100$ students. Find the median I.Q.

I.Q.	$55-64$	$65-74$	$75-84$	$85-94$	$95-104$	$105-114$	$115-124$	$125-134$	$135-144$
No. of students	$1$	$2$	$9$	$22$	$33$	$22$	$8$	$2$	$1$

Answer 1

Class interval ( Exclusive )	Class interval ( inclusive )	Class interval frequency	Cumulative Frequency
$55-64$	$54.5-64.5$	$1$	$1$
$65-74$	$64.5-74.5$	$2$	$3$
$75-84$	$74.5-84.5$	$9$	$12$
$85-94$	$84.5-94.5$	$22$	$34$ $\left(F\right)$
$95-104$	$94.5-104.5$	$33$ $\left(f\right)$	$67$
$105-114$	$104.5-114.5$	$22$	$89$
$115-124$	$114.5-124.5$	$8$	$97$
$125-134$	$124.5-134.5$	$2$	$99$
$135-144$	$134.5-144.5$	$1$	$100$
		$N=100$

We have $N=100$

$\frac{N}{2}=\frac{100}{2}=50$

The cumulative frequency just greater than $\frac{N}{2}$ is $67$ than the median class is $94.5-104.5$ such that,

$L=94.5,F=33,h=104.5-94.5=10$

$\Rightarrow$ $Median=L+\frac{\frac{N}{2}-F}{f}\times h$

$\Rightarrow$ $Median=94.5+\frac{50-34}{33}\times 10=94.5+4.88=99.5$

$\therefore$ $Median=99.4$