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Question

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

Class IntervalFrequency01051020x2030203040154050y50605Total60
[4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

Class Interval FrequencyCumulativeFrequency010551020x5+x20302025+x30401540+x4050y40+x+y5060545+x+yTotal60

n=60

45+x+y=60

x+y=6045

x+y=15(1)

The median is 28.5, which lies in the class 20 - 30

So, l = 20, f=20, cf=5+x, h=10

Median=l+(n2cff)×h

28.5=20+{602(5+x)20}×1028.5=20+25x2

25x2=28.52025x2=8.5

25x=8.5×225x=17

x=2517=8(2)

From (1) and (2), 8 + y = 15

y=158=7

Hence, the values of x and y are 8 and 7 respectively

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