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Question

The value of third quartile Q3 for the following distribution is

Marks
Group
510 1015 1520 2025 2530 3035 3540 4045
No. of
Students
5 6 15 10 5 4 2 1

A
15
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B
21.5
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C
25
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D
25.5
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Solution

The correct option is C 25
The cumulative frequency distribution is as given below
Marks
Groups (class)
No. of Students Cumulative
frequency
5-10 5 5
10-15 6 11
15-20 15 26
20-25 10 36
25-30 5 41
30-35 4 45
35-40 2 47
40-45 1 48
N=48

We have N=483N4=36
The cumulative frequency just greater than 3N4 is 41. The corresponding class is 2530. It is the upper quartile class.
l=25, f=5, h=5, F=36
Q3=l+3N4Ff×h=25+36365×5=25

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