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

Given Median =28.5

Then, median Class = 20 – 30

the lower limit (l) = 20

cumulative frequency of the class preceding 20 – 30 (cf) = 5 + x

frequency of the median class 20 – 30 = 20,

class size (h) = 10

Total frequencies (n) = 60

So, 45 + x + y = 60

⇒ x + y = 60 – 45

⇒ x + y = 15 …(i)

Using the formula,, we have

⇒8.5 × 2 = 25-x

⇒17 = 25 – x

⇒ x = 8

Putting the value of x in eq. (i), we get

⇒ 8 + y = 15

⇒ y = 15 – 8

⇒ y = 7