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 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?

Solution:

(i) Monthly wages of firm A = Rs 5253

Number of wage earners in firm A = 586

Therefore,

The total amount paid is 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 (σ_1²)

= 100

⇒ Standard deviation of the distribution of wages in firm A(σ₁)

= √100 = 10

⇒Variance of the distribution of wages in firm B (σ₁²)

= 121

⇒ Standard deviation of the distribution of wages in firm A(σ₁)

= √121 = 11

The mean of monthly wages of both the firms is same.

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

Thus, firm B has greater variability in the individual wages

NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.3 Question 3

An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results: (i) Which firm A or B pays larger amount as monthly wages? (ii) Which firm, A or B, shows greater variability in individual wages?

Solution:

From the given data, (i) Firm B pays the larger amount as monthly wages (ii) Firm B has greater variability in the individual wages