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Mathematics

CategoryWages in ₹ per dayNo. of workers
A502
B604
C708
D8012
E9010
F1006
G1108

(i) Calculate the mean wage, correct to nearest rupee.

(ii) If the number of workers in each category is doubled, what would be the new mean wage?

Measures of Central Tendency

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Answer

(i) We construct the following table:

Wages in ₹ per day (xi)No. of workers (fi)fixi
502100
604240
708560
8012960
9010900
1006600
1108880
Total504240

Mean = Total wageNo. of workers=fixifi=424050\dfrac{\text{Total wage}}{\text{No. of workers}} = \dfrac{∑fixi}{∑f_i} = \dfrac{4240}{50} = 84.8

Correcting to nearest rupee mean = ₹ 85

Hence, the mean wage is ₹ 85.

(ii) If the number of workers in each category is doubled then total wage will also be doubled.

New total wage = 4240 × 2 = 8480 and number of workers = 50 × 2 = 100.

Mean = New total wageNo. of workers=8480100\dfrac{\text{New total wage}}{\text{No. of workers}} = \dfrac{8480}{100} = 84.8

Correcting to nearest rupee mean = ₹ 85

Hence, the new mean wage is also ₹ 85.

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