Final answer:
The mean daily wages of the 50 workers is calculated using the midpoint method leading to a mean daily wage of Rs 545.2.
Step-by-step explanation:
Finding the Mean Daily Wages
To calculate the mean daily wages of the workers in the factory, we can use the midpoint method. First, we find the midpoint of each wage class by averaging the lower and upper limits. Then, we multiply each midpoint by the number of workers in that class to find the total wages for that class. Finally, we sum these totals and divide by the total number of workers to find the mean wage.
The distribution of daily wages and the number of workers is as follows:
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- 500–520: 12 workers
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- 520–540: 14 workers
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- 540–560: 8 workers
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- 560–580: 6 workers
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- 580–600: 10 workers
Let's calculate the midpoints (M) :
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- M1 = (500 + 520) / 2 = 510
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- M2 = (520 + 540) / 2 = 530
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- M3 = (540 + 560) / 2 = 550
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- M4 = (560 + 580) / 2 = 570
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- M5 = (580 + 600) / 2 = 590
Now, multiply each midpoint by the respective number of workers:
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- (510 × 12) = 6120
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- (530 × 14) = 7420
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- (550 × 8) = 4400
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- (570 × 6) = 3420
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- (590 × 10) = 5900
Summing all these products gives the total wages: 6120 + 7420 + 4400 + 3420 + 5900 = 27260
To find the mean daily wage, divide the total wages by the total number of workers:
Mean = Total Wages / Total Number of Workers = 27260 / 50 = 545.2
Therefore, the mean daily wage of the workers is Rs 545.2.