NCERT Solutions
Class 11 Maths
Sequences and Series

Ex.15.3 Q.3
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 wages earner |
586 |
648 |
|
Mean of monthly wages |
Rs 5253 |
Rs 5253 |
|
Variance of the distribution of wages |
100 |
121 |
(1) Which firm A or B pays larger amount as monthly wages?
(2) Which firm, A or B, shows greater variability in individual wages?
(1) Monthly wages of firm A = Rs 5253
Number of wage earners in firm A = 586
So, total amount paid = Rs 5253 × 586
Monthly wages of firm B = Rs 5253
Number of wage earners in firm B = 648
So, 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.
(2) 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 (σ2) = √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.