An analysis of monthly wages paid to workers in two firms A and B, bel

1.	An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:Firm AFirm BNo. of wage earners586648Mean of monthly wagesRs 5253Rs 5253Variance of the distribution of wages100121i) Which firm A or B pays larger amount as monthly wages?(ii) Which firm, A or B, shows greater variability in individual wages?
Answer» (i) Monthly wages of firm A = Rs 5253 Number of wage earners in firm A = 586 ∴Total amount paid = Rs 5253 × 586 Monthly wages of firm B = Rs 5253 Number of wage earners in firm B = 648 ∴Total amount paid = Rs 5253 × 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 (σ₁²) = 100 ∴ Standard deviation of the distribution of wages in firm A (( σ₁ ) = √100 = 10 Variance of the distribution of wages in firm = B ((σ₂²)) = 121 ∴ Standard deviation of the distribution of wages in firm B (σ₂²) = √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.

An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:Firm AFirm BNo. of wage earners586648Mean of monthly wagesRs 5253Rs 5253Variance of the distribution of wages100121i) Which firm A or B pays larger amount as monthly wages?(ii) Which firm, A or B, shows greater variability in individual wages?

Answer»

(i) Monthly wages of firm A = Rs 5253

Number of wage earners in firm A = 586

∴Total amount paid = Rs 5253 × 586

Monthly wages of firm B = Rs 5253

Number of wage earners in firm B = 648

∴Total amount paid = Rs 5253 × 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 (σ₁²) = 100

∴ Standard deviation of the distribution of wages in firm

A (( σ₁ ) = √100 = 10

Variance of the distribution of wages in firm = B ((σ₂²)) = 121

∴ Standard deviation of the distribution of wages in firm B (σ₂²) = √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.