Question

An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:

-	Firm A	Firm B
No. of wage earners	586	648
Mean of monthly wages	Rs 5253	Rs 5253
Variance of the distribution of wages	100	121

(i) Which firm A or B pays larger amount as monthly wages? 

(ii) Which firm, A or B, shows greater variability in individual wages?

Answer 1

(i) Monthly wages of firm A = Rs 5253 

Number of wage earners in firm A = 586 

∴Total amount paid = Rs 5253 x 586 

Monthly wages of firm B = Rs 5253 

Number of wage earners in firm B = 648 

∴Total amount paid = Rs 5253 x 648 

Thus, firm B pays the larger amount as monthly wages as the number of wage earners in firm B are more than the number of wage earners in firm A.

(ii) Variance of the distribution of wages in firm \(A(σ_1^2)=100\)

∴ Standard deviation of the distribution of wages in firm A ((σ₁) =√100=10

Variance of the distribution of wages in firm  \(B(σ_2^2)=121\)

∴ Standard deviation of the distribution of wages in firm \(B(σ_2^2)=√121=11\)

The mean of monthly wages of both the firms is same i.e., 5253. 

Therefore, the firm with greater standard deviation will have more variability.

Thus, firm B has greater variability in the individual wages.