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Mathematics

CategoryWages in ₹ per dayNo. of workers
A5002
B6004
C7008
D80012
E90010
F10006
G11008

(i) Calculate done mean wages correct to the nearest rupees.

(ii) If the number of workers in each categories double what would be the new mean wage?

Measures of Central Tendency

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Answer

(i) We construct the following table:

CategoryWages in ₹ per day (xi)No. of workers (fi)fixi
A50021000
B60042400
C70085600
D800129600
E900109000
F100066000
G110088800
TotalΣfi = 50Σfixi = 42400

Mean = ΣfixiΣfi\dfrac{Σfixi}{Σf_i}

= 4240050\dfrac{42400}{50}

= 848.

Hence, the mean wage is ₹ 848.

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

New total wage = 42400 × 2 = 84800 and number of workers = 50 × 2 = 100.

Mean = New total wageNo. of workers\dfrac{\text{New total wage}}{\text{No. of workers}}

= fixifi\dfrac{∑fixi}{∑f_i}

= 84800100\dfrac{84800}{100}​ = 848.

Hence, the new mean wage is also ₹ 848.

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