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Question

Construct the histogram for the following grouped frequency distribution.

Class intervals Frequency
0-35 42
36-50 30
51-60 20
61-100 48

A
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B
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C
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D
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Solution

The correct option is B
Data is presented in discrete grouped frequency distribution so first we have to convert it into continuous distribution.

Upper boundary of the first class = Lower boundary of the second class = 34+362 = 35 , similarily for others
Class intervals Class intervals
(Continous)
Frequency
1-35 0.5 - 35.5 42
36-50 35.5 - 50.5 30
51-60 50.5 - 60.5 20
61-100 60.5 - 100.5 48

Class length is varying so frequency per unit class has to be calculated and histogram has to be constructed with respective heights. For convenience least class length is taken as unit class length.

Modified length = Frequency of the classLength of that class×Least Class length
Class intervals Frequency Class length Modified Length
0.5 - 35.5 42 35 4235×10
=12
35.5 - 50.5 30 15 3015×10
=20
50.5 - 60.5 20 10 2010×10 =20
60.5 - 100.5 48 40 4840×10 =12

Choose suitable scale :
X-axis 1 cm = 1 Min. class interval
Y-axis 1 cm = 4 frequency unit

Plot the graph with the help of above table.

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