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Question

50 students of economics, secured the following marks in an examination:
Marks 20−25 25−30 30−35 35−40 40−45 45−50 50−55 55−60 60−65 65−70
Students 6 3 7 4 6 4 2 8 3 7
Calculate median.

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Solution

Marks Student
(f)
Cumulative Frequency
(c.f.)
20 − 25
25 − 30
30 − 35
35 − 40
40 − 45
45 − 50
50 − 55
55 − 60
60 − 65
65 − 70
6
3
7
4
6(f)
4
2
8
3
7
6
9
16
20 (c.f.)
26
30
32
40
43
50
N = ∑f = 50
Median class is given by the size of N2th item, i.e.502th item, which is 25th item.
This corresponds to the class interval of (40 45), so this is the median class.
Median=l1+N2-c.f.f×iso, Median=l1+502-c.f.f×ior, Median=40+25-206×5or, Median=40+256Thus, Median=40+4.16=44.16

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