6. An analysis of daily wages of casual labourers in two firms A and B, belonging to the
same industry, gives the following result:
Firm A
Firm B
50
60
No. of workers
Average daily wages (in 3)
S.D.
113
120
6.5
8.2
Find the mean and S.D. of wages of all casual labourers in the two firms taken together.
Answers
Answer:
(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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