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Question
Consider the following distribution of daily wages of 50 workers of a factory:
| Daily wages (in ₹) |
500-520 | 520-540 | 540-560 | 560-580 | 580-600 |
| Number of workers | 12 | 14 | 8 | 6 | 10 |
Find the mean daily wages of the workers of the factory by using an appropriate method.
Solution
To find the class mark for each interval, the following relation is used.
xi = `("Upper class limits + Lower class limits")/2`
Class size (h) of this data = 20
Taking 550 as assured mean (a), di, ui, and fiui can be calculated as follows:
| Daily wages (in Rs) |
Number of workers (fi) | xi | di = xi − 550 | ui = `d_i/20` | fiui |
| 500 - 520 | 12 | 510 | - 40 | − 2 | − 24 |
| 520 - 540 | 14 | 530 | - 20 | − 1 | − 14 |
| 540 - 560 | 8 | 550 | 0 | 0 | 0 |
| 560 - 580 | 6 | 570 | 20 | 1 | 6 |
| 580 - 600 | 10 | 590 | 40 | 2 | 20 |
| Total | ∑fi = 50 | - | - | -12 |
From the table, it can be observed that
∑fi = 50
∑fiui = −12
Mean, `barx = a+((∑f_i"u"_i)/(∑f_i))h`
`= 550+((-12)/50)20`
`= 550 - 24/5`
= 550 - 4.8
= 545.20
Therefore, the mean daily wage of the workers of the factory is Rs. 545.20.
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