If in a histogram the area of the rectangle is proportional to its frequency, can we say that the lengths of the rectangles are also proportional to the frequencies?

Histogram refers to the graphical representation of data using bars of different heights. Each bar shows data in the shape of a rectangle.

Answer: Yes. In a histogram, the area of the rectangle is proportional to its frequency, we can say that the lengths of the rectangles are proportional to the frequencies.

In a histogram, the shape of rectangles shows how different sets of data are represented as per the class intervals and frequency.

Explanation:

This can be understood through the following sequence of points.

• In a histogram, the rectangles so formed to represent any data depend on the class interval and the frequency.
• The area of the rectangle is proportional to the length of the rectangle.
• Since the area of the rectangle is proportional to its frequency,  the length of the rectangle and the frequency are proportional to each other.
• Hence the length of the rectangle is proportional to the frequencies. 

Therefore, the lengths of the rectangles in a histogram are proportional to the frequencies.