If the median of a distribution given below is 28.5 then, find the value of an x &y.

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

Given that median is 28.5 and \(n \ = \ \sum f_i \ = \ 60 \)

Here n = 60
\( \Rightarrow \ \frac{n}{2} \ = \ 30 \)

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

\(\therefore \) l = 20, h = 10, f = 20 and cf = 5 + x

\(\therefore \) median \(= \ l \ + \ ( \frac{ \frac{n}{2} \ - \ cf}{f} ) \ × \ h \)

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

\( \Rightarrow \ 57 \ = \ 40 \ + \ 25 \ - \ x \)

\( \Rightarrow \ x \ = \ 65 \ - \ 57 \ \)

\(\Rightarrow \ x \ = \ 8 \)

Also, 45 + x + y = 60
[ As n = 60 ]

\(\Rightarrow \ 45 \ + \ 8 \ + \ y \ = \ 60 \)

\(\Rightarrow \ y \ = \ 60 \ - \ 53 \ \)

\( \Rightarrow \ y \ = \ 7 \)

\(\therefore \) x = 8, y = 7