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Question

Following is the distribution of I.Q. of 100 students. Find the median I.Q.
I.Q.556465747584859495104
105114115124125134135144
No. of
students
129223322821

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Solution

Class interval
( Exclusive )
Class interval
( inclusive )
Class interval
frequency
Cumulative Frequency
556454.564.5 1 1
657464.574.5 2 3
7584 74.584.5912
859484.594.5 22 34 (F)
9510494.5104.5 33 (f) 67
105114104.5114.5 22 89
115124114.5124.5 8 97
125134124.5134.5 2 99
135144 134.5144.5 1 100
N=100
We have N=100

N2=1002=50

The cumulative frequency just greater than N2 is 67 than the median class is 94.5104.5 such that,

L=94.5,F=33,h=104.594.5=10

Median=L+N2Ff×h

Median=94.5+503433×10=94.5+4.88=99.5

Median=99.4

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