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Question

# The value of third quartile Q3 for the following distribution is MarksGroup 5âˆ’10 10âˆ’15 15âˆ’20 20âˆ’25 25âˆ’30 30âˆ’35 35âˆ’40 40âˆ’45 No. ofStudents 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 25The 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=48⇒3N4=36The cumulative frequency just greater than 3N4 is 41. The corresponding class is 25−30. It is the upper quartile class.∴l=25, f=5, h=5, F=36∴Q3=l+3N4−Ff×h=25+36−365×5=25

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