Question

The following table gives the marks obtained by $300$ students of a management course. Find the median of the distribution.

Marks obtained	No. of Students
$0-15$	$26$
$15-30$	$34$
$30-45$	$64$
$45-60$	$76$
$60-75$	$60$
$75-90$	$30$
$90-100$	$10$

• A. $62.96$ marks
• B. $62.13$ marks
• C. $50.13$ marks
• D. $50.96$ marks

Answer 1

The correct option is C $50.13$ marks

Marks obtained	No. of students(f)	Cumulative frequency
$0-15$	$26$	$26$
$15-30$	$34$	$60$
$30-45$	$64$	$124$
$45-60$	$76$	$200$
$60-75$	$60$	$260$
$75-90$	$30$	$290$
$90-100$	$10$	$300$

Since $N/2=150$, therefore, $45-60$ is the median class.
Further, $L_m=45,f_m=76,h=60-45=15$ and $C=124$
$\frac{45+(150-124)}{76}\times 15=50.13$.