Question

For a histogram based on a frequency distribution with unequal class intervals, the frequency of a class should be proportional to:
1. the height of the rectangle.
2. the area of the rectangle.
3. the width of the rectangle.
4. the perimeter of the rectangle.

Answer 1

Correct Answer - Option 2 : the area of the rectangle.

Concept:

• When constructing a histogram with non-uniform (unequal) class widths, we must ensure that the areas of the rectangles are proportional to the class frequencies.
• Remember that the histogram differs from a bar chart in that it is the area of the bar that denotes the value, not the height. This means that we would need to consider the widths in order to determine the height of each rectangle.

 

Calculation:

From the definition of histogram, it is clear that the frequency of a class is proportional to the area of the rectangle, and NOT to its height.