From the data, given below, calculate the mean wage, correct to the nearest rupee.

Category	Wages in ₹/day	No. of workers
A	50	2
B	60	4
C	70	8
D	80	12
E	90	10
F	100	6

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

(ii) If the wages per day in each category are increased by 60%; what is the new mean wage ?

(iii) 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 ?

Mean = $\dfrac{Σfx}{Σf} = \dfrac{3360}{42}$ = 80.

(i) Original mean = $\dfrac{Σfx}{Σf}$

If no. of workers is doubled, then

New mean = $\dfrac{2Σfx}{2Σf} = \dfrac{Σfx}{Σf}$ = original mean.

∴ If the numbers of workers in each category is doubled, then new mean wage will remain same.

Hence, mean = 80.

(ii) If the wages per day in each category are increased by 60% then new mean wage also increases by 60%.

New mean = 80 + $\dfrac{60}{100} \times 80$

= 80 + 48 = 128.

Hence, new mean = 128.

(iii) There will be no change in mean due to change in number of workers.

If wages is reduced by 40% then, mean will also reduce by 40%.

New mean = 80 - $\dfrac{40}{100} \times 80$

= 80 - 32

= 48.

Hence, new mean = 48.