Construct the histogram for the following grouped frequency distribution.

Class intervals Frequency

0-35 42

35-50 30

50-60 20

60-100 48

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Solution

The correct option is B
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 = $\frac{Frequency of the class}{Length of that class} \times Least Class length$

Class intervals Frequency Class length Modified Length

0-35 42 35 $\frac{42}{35} \times 10$
=12

35-50 30 15 $\frac{30}{15} \times 10$
=20

50-60 20 10 $\frac{20}{10} \times 10$ =20

60-100 48 40 $\frac{48}{40} \times 10$ =12

Choose suitable scale :
X-axis 1 division = 10 class interval unit
Y-axis 1 division = 4 frequency unit

Now we draw the rectangles with class intervals as bases and the corresponding frequencies as the corresponding heights.
$∴$ Histogram for the givendata is:

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