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If the median of the distribution given below is 28.5, find the value of `x` and `y` . Class interval: 0-10 10-20 20-30 30-40 40-50 50-60 No. of students: 5 `x` 20 15 `y` 5

Text Solution

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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`
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