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Question
The following are the marks (out of 100) of 60 students in mathematics.
16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35, 72, 55, 75, 31, 52, 28, 72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55, 26, 95, 31, 7, 78, 92, 62, 52, 56, 15, 63, 25, 36, 54, 44, 47, 27, 72, 17, 4, 30.
Construct a grouped frequency distribution table with width 10 of each class starting from 0 – 9.
Solution
First, arranging the given data in ascending order.
4, 5, 7, 7, 13, 15, 16, 16, 17, 17, 19, 24, 25, 26, 27, 28, 30, 31, 31, 34, 34, 35, 35, 36, 36, 36, 42, 44, 45, 47, 48, 51, 52, 52, 54, 55, 55, 56, 56, 61, 62, 62, 63, 68, 70, 72, 72, 72, 74, 75, 75, 78, 80, 81, 85, 86, 86, 92, 95, 97.
We arrange the given data into groups like 0 – 9, 10 – 19, 20 – 29, ... The class width in each case is 10.
The frequency distribution of the given data is given below:
| Class interval | Tally marks | Frequency |
| 0 – 9 | `bb|bb|bb|bb|` | 4 |
| 10 – 19 | `\cancel(bb|bb|bb|bb|) bb|bb|` | 7 |
| 20 – 29 | `\cancel(bb|bb|bb|bb|)` | 5 |
| 30 – 39 | `\cancel(bb|bb|bb|bb|) \cancel(bb|bb|bb|bb|)` | 10 |
| 40 – 49 | `\cancel(bb|bb|bb|bb|)` | 5 |
| 50 – 59 | `\cancel(bb|bb|bb|bb|) bb|bb|bb|` | 8 |
| 60 – 69 | `\cancel(bb|bb|bb|bb|)` | 5 |
| 70 – 79 | `\cancel(bb|bb|bb|bb|) bb|bb|bb|` | 8 |
| 80 – 89 | `\cancel(bb|bb|bb|bb|)` | 5 |
| 90 – 99 | `bb|bb|bb|` | 3 |
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