Question

If the median of the distribution given below is $28.5$, find the value of x and y.

Class interval:	0-10	10-20	20-30	30-40	40-50	50-60
No. of students:	5	x	20	15	y	5

Answer 1

Computation of Median

Class interval Frequency (f) Cumulative frequency(cf)

0-10 5 5

10-20 x 5+x

20-30 20 25+x

30-40 15 40+x

40-50 y 40+x+y

50-60 5 45+x+y

$\sum f_1=60$

We have, Median = $28.5$

Clearly, It lies in the class interval $20-30$. So, $20-30$ is the median class.

$\therefore l=20,h=10,f=20,F=5+x$ and $N=60$

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

$\Rightarrow 28.5=20+\frac{30-(5+x)}{20}\times 10$

$\Rightarrow 28.5=20+\frac{25-x}{2}$

$\Rightarrow 8.5=\frac{25-x}{2}\Rightarrow 25-x=17\Rightarrow x=8$

We have,

$N=60$

$\therefore 45+x+y=60\Rightarrow x+y=15$

Putting $x=8$ in$x+y=15$, we get $y=7$

Hence, $x=8$ and $y=7$.