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

Explanation

it can be observed that `n = 60 `
n/2 = 30
`45 + x + y = 60`
`x + y = 15 `.....(i)
The median of the data is given as `28.5` which lies in interval `20 − 30.`
Therefore, median class = `20 - 30`
Class size, `h = 10`
Lower limit of median class, `l = 20`

Frequency of median class, `f = 20`
Cumulative frequency of class preceding the median class, cf = 5 + x
Median` = l + [(n/2 - cf)/f] xx h`
`28.5 = 20 + [(60/2 - (5 + x))/20] xx 10`

`8.5 = (25 - x)/2`

`25 - x = 8.5 xx 2`

`x = 25 - 17`
`x = 8`

Putting `x = 8` in equation (i)
`8 + y = 15`

`y = 7`