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Question

Calculate the median from the following data:
Marks Frequency
Less than 10 5
Less than 20 20
Less than 30 45
Less than 40 80
Less than 50 100
Less than 60 115
Less than 70 125
Less than 80 130

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Solution

Marks Class Interval Frequency
(f)
Cumulative Frequency (c.f.)
Less than 10
Less than 20
Less than 30
0 − 10
10 − 20
20 − 30
5
15
25
5
20
45 c.f
Less than 40 30 − 40 (f) 35 80
Less than 50
Less than 60
Less than 70
Less than 80
40 − 50
50 − 60
60 − 70
70 − 80
20
15
10
5
100
115
125
130
N=f=130

Median class is given by the size of N2th item, i.e.1302th item, which is 65th item.
This corresponds to the class interval of 30 − 40, so this is the median class.
Median=l1+N2-c.f.f×iso, Median=l1+1302-c.f.f×ior, Median=30+65-4535×10or, Median=30+5.71=35.71Thus, Median=35.71

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