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?

Question

Let $X=\{x\in\mathbb{N}:1\le x\le19\}$ and for some $a,b\in\mathbb{R}$, $Y=\{ax+b:x\in X\}$. If the mean and variance of the elements of $Y$ are $30$ and $750$ respectively, then the sum of all possible values of $b$ is

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 ((Ïƒ₁) =√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.

Solution and Explanation

Top Questions on Variance and Standard Deviation

Questions Asked in CBSE Class XI exam

-	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