Question

Draw a histogram to represent the following data.

Clas interval	10−14	14−20	20−32	32−52	52−80
Frequency	5	6	9	25	21

Answer 1

In the given frequency distribution, class sizes are different.
So, we calculate the adjusted frequency for each class.
The minimum class size is 4.
Adjusted frequency of a class =$\frac{\mathrm{Minimum}\mathrm{class}\mathrm{size}}{\mathrm{Class}\mathrm{size}\mathrm{of}\mathrm{the}\mathrm{class}}\times \mathrm{Its}\mathrm{frequency}$

We have the following table:

Class Interval	Frequency	Adjusted Frequency
10-14	5	$\frac{4}{4}\times 5=5$
14-20	6	$\frac{4}{6}\times 6=4$
20-32	9	$\frac{4}{12}\times 9=3$
32-52	25	$\frac{4}{20}\times 25=5$
52-80	21	$\frac{4}{28}\times 21=3$

We mark the class intervals along the x-axis and the corresponding adjusted frequencies along the y-axis.
We have chosen the scale as follows:
On the x- axis,
1 big division = 5 units
On the y-axis,
1 big division = 1 unit
We draw rectangles with class intervals as the bases and the corresponding adjusted frequencies as the heights.
Thus, we obtain the following histogram: