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प्रश्न
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
| Weight (in kg) | 40−45 | 45−50 | 50−55 | 55−60 | 60−65 | 65−70 | 70−75 |
| Number of students | 2 | 3 | 8 | 6 | 6 | 3 | 2 |
उत्तर
The cumulative frequencies with their respective class intervals are as follows
| Weight (in kg) | Frequency (fi) | Cumulative frequency |
| 40 − 45 | 2 | 2 |
| 45 − 50 | 3 | 2 + 3 = 5 |
| 50 − 55 | 8 | 5 + 8 = 13 |
| 55 − 60 | 6 | 13 + 6 = 19 |
| 60 − 65 | 6 | 19 + 6 = 25 |
| 65 − 70 | 3 | 25 + 3 = 28 |
| 70 − 75 | 2 | 28 + 2 = 30 |
| Total (n) | 30 |
Cumulative frequency just greater than `N/2 (i.e 30/2 = 15)` is 19, belonging to class interval 55 − 60.
Median class = 55 − 60
Lower limit (l) of median class = 55
Frequency (f) of median class = 6
Cumulative frequency (cf) of median class = 13
Class size (h) = 5
Median = `l + ((N/2 - cf)/f) xx h`
= `55 + ((15-13)/6) xx 5`
= `55 + 10/6`
= 55 + 1.66
= 56.67
Therefore, the weight is 56.67 kg.
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