Question

The percentage of marks obtained by the studentsin a class of $50$ are given below. Find the median for the following data.

Marks$\left(\%\right)$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
Number of students	$6$	$12$	$14$	$8$	$6$	$4$

• A. $65$
• B. $63.5$
• C. $64.5$
• D. $65.5$

Answer 1

The correct option is A $65$

Marks$\left(\%\right)$ Number of students(f) Cumulative frequency(cf)

$40-50$ $6$ $6$

$50-60$ $12$ $18$

$60-70$ $14$ $32$

$70-80$ $8$ $40$

$80-90$ $6$ $46$

$90-100$ $4$ $50$

Median is $25,26$

Median$=l+\frac{\frac{n}{2}-cf}{f}\times h$

where the lower limit,(l) of median class$=60$

the number of observations,$\left(n\right)=50$

the cumulative frequency of class preceding the median class,$\left(cf\right)=18$

the frequency of median class,$\left(f\right)=14$ class size $\left(h\right)=10$

Substituting the above values in the formula, we get

Median $=60+\frac{\frac{50}{2}-18}{14}\times 10$

$=60+0.5\times 10$

$=65$

Therefore, the median of the above data is $65$