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Question 2
If the median of the distribution is given below is 28.5, find the values of x and y. 

Class intervalFrequency01051020x2030203040154050y50605Total60


Solution

We may find the cumulative frequency for the given data as following:

Class intervalFrequencyCumulative frequency010551020x5+x20302025+x30401540+x4050y40+x+y5060545+x+yTotal(n)60 

It is clear that n = 60

45 + x + y = 60

x + y = 15 (1)

Median of data is given as 28.5 which lies in interval 20 - 30.

So, median class = 20 - 30

Lower limit l of median class = 20

Cumulative frequency cf of class preceding the median class = 5 + x

Frequency f of median class = 20

Class size h = 10

Now, median=1+(n2cff)×h28.5=20+[602(5+x)20]×108.5=(25x2)

17 = 25 - x

x = 8

From equation (1)

8 + y = 15

y = 7

Hence values of x and y are 8 and 7 respectively.

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