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प्रश्न
The following table gives the marks scored by a set of students in an examination. Calculate the mean of the distribution by using the short cut method.
| Marks | Number of Students (f) |
| 0 – 10 | 3 |
| 10 – 20 | 8 |
| 20 – 30 | 14 |
| 30 – 40 | 9 |
| 40 – 50 | 4 |
| 50 – 60 | 2 |
उत्तर
Let assumed mean A = 25
| C.I. marks |
xi | fi | di = xi – A | fidi |
| 0 – 10 | 5 | 3 | – 20 | – 60 |
| 10 – 20 | 15 | 8 | – 10 | – 80 |
| 20 – 30 | 25 = A | 14 | 0 | 0 |
| 30 – 40 | 35 | 9 | 10 | 90 |
| 40 – 50 | 45 | 4 | 20 | 80 |
| 50 – 60 | 55 | 2 | 30 | 60 |
| n = 40 | `sumf_i d_i` = 90 |
Mean = `A + (sumf_i d_i)/n`
= `25 + 90/40`
= 25 + 2.25
= 27.25 marks
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| Class | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 | 100 - 120 |
| Frequency | 20 | 35 | 52 | 44 | 38 | 31 |
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| Age (in years) | 18 – 24 | 24 – 30 | 30 – 36 | 36 – 42 | 42 – 48 | 48 – 54 |
| Number of workers | 6 | 8 | 12 | 8 | 4 | 2 |
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| Class | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
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