Explanation:

Histogram is a graphical representation of data that uses bars to represent the frequency distribution of a set of continuous or discrete data. The height of each bar represents the frequency or the number of times a value falls within a certain range or class interval.

In a histogram, the width of each bar is proportional to the size of the class interval or range. If the classes are of unequal width, then the heights of the rectangles must be proportional to the frequency densities.

Frequency density is defined as the frequency of a particular class divided by the width of the class interval. The height of each bar in a histogram is proportional to the frequency density, not the frequency itself.

For example, consider a histogram with the following class intervals and frequencies:

Class interval Frequency
0-10 5
11-20 10
21-30 15

The width of the first class interval is 10, the second is 10 and the third is 10. However, the frequency of each class interval is different. Therefore, the heights of the rectangles must be proportional to the frequency densities.

The frequency densities can be calculated as follows:

Class interval Frequency Width Frequency density
0-10 5 10 0.5
11-20 10 10 1.0
21-30 15 10 1.5

The height of each rectangle should be proportional to the frequency density. Therefore, the height of the first rectangle should be 0.5 times the height of the second rectangle and 0.75 times the height of the third rectangle.

Conclusion:

Hence, it can be concluded that if the classes of unequal width then the heights of the rectangles must be proportional to the frequency densities.