Question

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

Class-interval	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	Total
Frequency	$5$	$x$	$20$	$15$	$y$	$5$	$60$

Answer 1

Here, it is given that Median $=28.5$ and $n=\sum f_i=60$

Cummulative frequency table for the following data is given.

Here $n=60\Rightarrow \frac{n}{2}=30$

Since, median is $28.5$, median class is $20-30$

Hence, $l=20,h=10,f=20,c.f.=5+x$

Therefore, Median $=l+(\frac{\frac{n}{2}-cf}{f})h$

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

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

$\Rightarrow 8.5\times 2=25-x$

$\Rightarrow x=8$

Also, $45+x+y=60$

$\Rightarrow y=60-45-x=15-8=7$.

Hence, $x=8,y=7$