If the median of a distribution given below is 28.5, find the value of 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 data, n = 60

Median of the given data = 28.5

Where, $\frac{n}{2}$ = 30

Median class is 20 – 30 with a cumulative frequency = 25+x

Lower limit of median class, l = 20,

C_f = 5+x,

f = 20 & h = 10

Substitute the values

28.5=20+($\frac{30-5-x}{20}$) × 10

8.5 = $\frac{25-x}{2}$

17 = 25-x

Therefore, x =8

Now, from cumulative frequency, we can identify the value of x + y as follows:

Since,

60=5+20+15+5+x+y

Now, substitute the value of x, to find y

60 = 5+20+15+5+8+y

y = 60-53

y = 7

Therefore, the value of x = 8 and y = 7.