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प्रश्न
If the class intervals of a frequency distribution are 5 - 12, 13 - 20, 21 - 28, 29 - 36, 37 - 44, 45 - 52 and 53 - 60, find the following:
(i) The class limits and class boundaries of 21 - 28
(ii) The class size and the class mark of the class interval 45 - 52.
(iii) Find the true class limits of all the class intervals.
उत्तर
(i) Here, the lower limit is 21 and the upper limit is 28.
The actual lower limit = 21 - 0.5 = 20.5
The actual upper limit = 28 + 0.5 = 28.5
∴ The class boundaries are 20.5 and 28.5.
(ii) For the class 45 - 52,
The actual class limiits are 45 - 0.5 = 44.5 and 52 + 0.5 = 52.5
∴ The class size of this class
= 52.5 - 44.5
= 8
∴ The class mark of this class
= `(1)/(2)(44.5 + 52.5)`
= 48.5.
(iii) As the classes are exclusive, so the true class limits are the same as the class limits.
| Class | True class limits |
| 5 - 12 | 4.5 - 12.5 |
| 13 - 20 | 12.5 - 20.5 |
| 21 - 28 | 20.5 - 28.5 |
| 29 - 36 | 28.5 - 36.5 |
| 37 - 44 | 36.5 - 44.5 |
| 45 - 52 | 44.5 - 52.5 |
| 53 - 60 | 52.5 - 60.5 |
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