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Question

Find the median for the following data given below:
X
47
710
1013
1314
F
2
5
3
2

A
11
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B
10
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C
9
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D
8
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Solution

The correct option is C 9
X
F(f)
Cumulative frequency (cf)
47
2
2
710
5
2+5=7
1013
3
7+3=10
1314
2
10+2=12

n=Σf=12
n2=122=6

Median =l+(n2cff)×h
n=Σf= total number of frequency =12
n2=122=6
So, the median class is 1013
L= Lower limit of median class =10
cf= Cumulative frequency of the class preceding the median class =7
f= frequency of the median class =3
h= class width =3
Therefore, Median =l+⎜ ⎜n2cff⎟ ⎟×h
=10+⎜ ⎜ ⎜12273⎟ ⎟ ⎟×3
=10+(673)×3
=101
=9
Hence, the median is 9

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