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In a histogram, the areas of the rectangles are proportional to the frequencies. Can we say that the lengths of the rectangles are also proportional to the frequencies?

Solution:

A histogram is the graphical representation of data where data is grouped into continuous number ranges and each range corresponds to a vertical bar.

1. The horizontal axis displays the number range.

2. The vertical axis (frequency) represents the amount of data that is present in each range.

We know that

1. In a histogram, rectangles formed to represent data depend on the frequency and class interval.

2. The length of the rectangle is proportional to its area.

3. Area is proportional to its frequency, length of rectangle and frequency are proportional to each other.

4. So length is proportional to frequency.

Therefore, the lengths of the rectangles are proportional to the frequencies only when the class sizes are the same.

✦ Try This: In a sample study of 630 people, it was found that 322 people have a high school certificate. If a person is selected at random, the probability that the person has a high school certificate is :

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14

NCERT Exemplar Class 9 Maths Exercise 14.2 Sample Problem 2

In a histogram, the areas of the rectangles are proportional to the frequencies. Can we say that the lengths of the rectangles are also proportional to the frequencies?

Summary:

In a histogram, the areas of the rectangles are proportional to the frequencies. No, the lengths of the rectangles are also proportional to the frequencies only when the class sizes are the same

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