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

## Solution :

Here, it is given that median is 28.5

and n = 60

We now prepare the following cumulative frequency table :

Here, n = 60 So, $$n\over 2$$ = 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 + ($${n\over 2} – cf\over f$$) $$\times$$ h

$$\implies$$ 28.5 = 20 + $$30 – (5 + x)\over 20$$ $$\times$$ 10

$$\implies$$ 57 = 40 + 28 – x $$\implies$$ x = 65 – 57 = 8

Also, 45 + x + y = 60

So, y = 7

Hence, x = 8 and y = 7.