Question

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

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

Answer 1

Given:

Median $=28.5$ and $n=\sum f_i=60$

We have, $n=60$

$⟹\frac{n}{2}=30$

Since the median is given to be $28.5$, thus the median class is $20–30$.

Therefore

$\frac{n}{2}=30,l=20,f=20,cf=5+x,$ and $h=10$

Substituting these values in the formula

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

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

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

$\Rightarrow 57=40+25-x$

$\Rightarrow x=8$

Also,

$45+x+y=60$

with $x=8,$ we get

$y=7$

Hence, $(x,y)=(8,7)$