Question

Construct the histogram for the following grouped frequency distribution.

Class intervals	Frequency
1-35	25
36-50	16
51-60	10
61-100	40

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

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 = $\frac{34+36}{2}$ = 35 , similarily for others

Class intervals	Class intervals (Continuous)	Frequency
1-35	0.5 - 35.5	25
36-50	35.5 - 50.5	16
51-60	50.5 - 60.5	10
61-100	60.5 - 100.5	40

Class length is varying in the given distribution, in such case 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 = $\frac{\text{Frequency of the class}}{\text{Length of that class}}\times \text{Least Class length}$

Class intervals	Frequency	Class length	Modified Length
0.5-35.5	70	35	$\frac{70}{35}\times 10$ =20
35.5 - 50.5	15	15	$\frac{15}{15}\times 10$ =10
50.5 - 60.5	20	10	$\frac{20}{10}\times 10$ =20
60.5 - 100.5	40	40	$\frac{40}{40}\times 10$ =10

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

Plot the graph with the help of above table.