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Question

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?


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Solution

Define a histogram and its properties

  1. A graph, where a set of rectangles are represented as per the class intervals and the frequencies, is called a histogram.
  2. The X-axis represents the class intervals and the Y-axis represents the frequencies.
  3. A rectangle is drawn considering class intervals as base and frequencies as height.
  4. If the intervals are equal then the area of the rectangle is directly proportional to frequency.

For example:

Let, us understand with the help of an example.

Let, the below diagram show a histogram with data of marks obtained by 30 students in a test.

Here, the X-axis represents the class intervals of marks and the Y-axis represents the number of students (i.e., frequencies).

As it can be seen, in the adjoining diagram, each class interval has the same width, i.e., 10 units.

So, the change in the area of each rectangle will depend on its length only.

Then, it is clear that the higher the frequency larger the area of the rectangle.

Thus, the area of the rectangle is proportional to its frequency.

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


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