The following table gives the wages of different categories of workers in a factory :

Category	Wages in ₹/day	Number of workers
A	250	2
B	300	4
C	350	8
D	400	12
E	450	10
F	500	6
G	550	8

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

(i) We know that,

n = ∑f = 50.

By formula,

Mean wage = $\dfrac{\sum fx}{n} = \dfrac{21200}{50}$ = ₹ 424

Hence, mean wage is ₹ 424.

(ii) If all frequencies in a distribution are multiplied by a constant, the mean remains unchanged.

n = ∑f = 50 x 2 = 100.

∑fx = 21200 x 2 = 42400

By formula,

Mean wage = $\dfrac{\sum fx}{n} = \dfrac{42400}{100}$ = ₹ 424

Hence, new mean wage is ₹ 424.