(a) An analysis of monthly wages paid to the workers of two firms A and B gives the following results: Firm A 500 186 81 Firm B 600 175 100 No. of workers Average daily wage Variance of distribution of wages (i) In which firm A or B, is greater variability in individual wages? (ii) Calculate Average daily wage of all workers in both the firms A and B.
Answers
Answer:
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 ?
Step-by-step explanation:
(i) Number of wage earner in firm A=586
Mean of monthly wage of firm A=Rs5253
Mean of monthly age of firm A =
No. of wage earners in firm A
Total amount paid
5253=
586
Total amount paid
Total amount paid by Firm A =5253×586
Number of wage earner in firm B=648
Mean of monthly wage of firm B=Rs5253
Mean of monthly age of firm B =
No. of wage earners in firm B
Total amount paid
5253=
648
Total amount paid
Total amount paid by Firm B =5253×648
Clearly, firm B paid larger amount as monthly wage.
(ii) Variance of the distribution of wages in firm A (σ
1
2
)=100
∴ Standard deviation of the distribution of wages in firm A(σ
1
)=
100
=10
Variance of the distribution of wages in firm B(σ
1
2
)=121
∴ Standard deviation of the distribution of wages in firm B(σ
2
)=
121
=11
The mean of monthly wages of both the firms is same i.e.5253. So, the firm with greater standard deviation will have more variability.
Thus firm B has greater variability in the individual wages
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