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Question
The following table gives the wages of worker in a factory:
| Wages in ₹ | 45 - 50 | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 |
| No. of Worker's | 5 | 8 | 30 | 25 | 14 | 12 | 6 |
Calculate the mean by the short cut method.
Solution
| Class Interval | Frequency `f_i` |
Observation (mid value) `x_i` |
`d_i = x_i - A` | `f_id_i` |
| 45 - 50 | 5 | 47·5 | -15 | -75 |
| 50 - 55 | 8 | 52·5 | -10 | -80 |
| 55 - 60 | 30 | 57·5 | -5 | -150 |
| 60 - 65 | 25 | 62·5 = A | 0 | 0 |
| 65 - 70 | 14 | 67·5 | 5 | 70 |
| 70 - 75 | 12 | 72·5 | 10 | 120 |
| 75 - 80 | 6 | 77·5 | 15 | 90 |
| `sumf_i` = 100 | `sum f_i d_i` = -25 |
Mean `bar"X" = "A" + (sumf_i d_i)/(sumf_i)`
= `62·5 + (-25)/(100)` = 62·25.
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