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प्रश्न
Calculate the mean of the distribution given below using the shortcut method.
| Marks | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 | 61-70 | 71-80 |
| No. of students | 2 | 6 | 10 | 12 | 9 | 7 | 4 |
उत्तर
Let A be the assumed mean and d be the deviation of x from the assumed mean.
Let A = 45.5.
d = x – A
| Marks (C.I.) | No. of students (Frequency f) |
Mid-point of C.I. (x) |
d = x – A | f × d |
| 11-20 | 2 | 15.5 | -30 | -60 |
| 21-30 | 6 | 25.5 | -20 | -120 |
| 31-40 | 10 | 35.5 | -10 | -100 |
| 41-50 | 12 | 45.5 | 0 | 0 |
| 51-60 | 9 | 55.5 | 10 | 90 |
| 61-70 | 7 | 65.5 | 20 | 140 |
| 71-80 | 4 | 75.5 | 30 | 120 |
| `sumfd = 70` |
Mean = `A + (sumfd)/(sum f)`
`=> Mean = 45.5 + 70/50`
`=> Mean = 45.5 + 1.4`
`:. Mean = 45.9`
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