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Question

Given the following data, find out median:
Age 20−25 25−30 30−35 35−40 40−45 45−50 50−55 55−60
Number of Students 50 70 100 180 150 120 70 60

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Solution

Age No. of Students
(f)
Cumulative Frequency
(c.f.)
20 − 25
25 − 30
30 − 35
35 − 40
40 − 45
45 − 50
50 − 55
55 − 60
50
70
100
180 (f)
150
120
70
60
50
120
220 (c.f.)
400
550
670
740
800
N = ∑f = 800
Median class is given by the size of N2th item, i.e.8002th item, which is 400th item.
This corresponds to the class interval of (35 40), so this is the median class.
Median=l1+N2-c.f.f×iso, Median=l1+8002-c.f.f×ior, Median=35+400-220180×5or, Median=35+180180×5Thus, Median=35+5=40

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