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Question
From the data given below, calculate the mean wage, correct to the nearest rupee.
| Category | A | B | C | D | E | F |
| Wages (Rs/day) | 50 | 60 | 70 | 80 | 90 | 100 |
| No. of workers | 2 | 4 | 8 | 12 | 10 | 6 |
- If the number of workers in each category is doubled, what would be the new mean wage?
- If the wages per day in each category are increased by 60%; what is the new mean wage?
- If the number of workers in each category is doubled and the wages per day per worker are reduced by 40%, what would be the new mean wage?
Solution
| Wages (Rs/day) (x) |
No. of Workers (f) |
fx |
| 50 | 2 | 100 |
| 60 | 4 | 240 |
| 70 | 8 | 560 |
| 80 | 12 | 960 |
| 90 | 10 | 900 |
| 100 | 6 | 600 |
| Total | 42 | 3360 |
`barx = (sumfx)/(sumf)`
= `3360/42`
= 80
i. Mean remains the same if the number of workers in each category is doubled
Mean = 80
ii. Mean will be increased by 60% if the wages per day per worker is increased by 60%
New mean = `80 xx 160/100 = 128`
iii. No change in the mean if the number of workers is doubled but if wages per worker is reduced by 40%, then
New mean = `80 xx 60/100 = 48`
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