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Question
The frequency distribution has been represented graphically as follows:
| Marks | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 100 |
| Number of Students | 10 | 15 | 20 | 25 |
Do you think this representation is correct? Why?
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Solution
No, here the widths of the rectangles are varying, so we need to make certain modifications in the length of the rectangles so that the areas are proportional to the frequencies.
We proceed as follows:
1. Select a class interval with the minimum class size, here the minimum class size is 20.
2. The length of the rectangles are then modified to be proportionate to the class size 20.
Now, we get the following modified table:
| Marks | Number of students (Frequency) |
Width of the class |
Length of the rectangle |
| 0 – 20 | 10 | 20 | `10/20 xx 20 = 10` |
| 20 – 40 | 15 | 20 | `15/20 xx 20 = 15` |
| 40 – 60 | 20 | 20 | `20/20 xx 20 = 20` |
| 60 – 100 | 25 | 40 | `25/40 xx 20 = 12.5` |
So, the correct histogram with varying width is given below:
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