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Question
The marks obtained (out of 100) by a class of 80 students are given below:
| Marks | Number of students |
| 10 – 20 | 6 |
| 20 – 30 | 17 |
| 30 – 50 | 15 |
| 50 – 70 | 16 |
| 70 – 100 | 26 |
Construct a histogram to represent the data above.
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Solution
See the given table, the class intervals are of unequal width.
So, we calculate the adjusted frequency for each class.
Now, minimum size = 20 – 10 = 10
The formula of adjusted frequencies are:
Adjusted frequency = `("Minimum class" - "size")/("Class" - "size") xx` Frequency of the class
Now, the modified table for frequency distribution is given by:
| Marks | Numbers of students (Frequency) |
Adjusted frequency |
| 10 – 20 | 6 | `10/10 xx 6 = 6` |
| 20 – 30 | 17 | `10/10 xx 17 = 17` |
| 30 – 50 | 15 | `10/20 xx 15 = 15/2 = 7.5` |
| 50 – 70 | 16 | `10/20 xx 16 = 16/2 = 8` |
| 70 – 100 | 26 | `10/30 xx 26 = 26/3 = 8.67` |
Now, let’s construct rectangles with class limits as base and respective adjusted frequencies as height
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