Question

Following are marks obtained in Mathematics by students of Class X.

Marks obtained	0-10	10-20	20-30	30-40	40-50	50-60	60-70
No. of students	$2$	$10$	$12$	$15$	$13$	$8$	$4$

Find the median of the marks obtained in Mathematics.

Answer 1

$C.I.$	$f$	$cf$
0 - 10	2	2
10 - 20	10	12
20 - 30	12	24
30 - 40	15	39
40- 50	13	52
50 - 60	8	60
60 - 70	4	64

Above frequency distribution table can be formed from the given data.

To find median, we need to find the median class first,

Total no of students$\left(N\right)=64$

$\Rightarrow \frac{N}{2}=\frac{64}{2}=32$

From the $cf$ column of the table, we can see that $32$ is more than $24$ and less than $39$.

So, median class will be $30-40$

Now, we know that

$Median=l+\frac{(\frac{N}{2}-C)}{f}\times h$

where, $l=$ lower limit of median class $=30$,

$C=$ cumulative frequency of class preceding the median class $=24$,

$f=$ frequency of the median class $=15$,

$h=$ class size $=10$

$\therefore Median=30+\frac{32-24}{15}\times 10$

$=30+\frac{8}{15}\times 10$

$=30+5.33=35.33$

Hence, the median marks obtained by the students are $35.33$.