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Question

Find out median marks of the following marks distribution for 100 students.
Marks 0−10 10−20 20−30 30−40 40−50
Number of Students 8 30 40 12 10

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Solution

Marks No. of students Cumulative frequency
0 − 10
10 − 20
8
30
8
8 + 30 = 38 (c.f.)
20 − 30 40 (f) 38 + 40 = 78
30 − 40
40 − 50
12
10
78 + 12 = 90
90 + 10 = 100
N = 100

Median or M = Size of N2th item
or, M = Size of 1002th item
or, M = Size of 50th item

Hence, median lies in the class 20-30
Median=l1+N2-c.ff×i or, M =20+50-3840×10 or, M =20 + 12040 or, M =20 + 3 M= 23 marks

Hence, the median marks is 23.

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