13) A factory has 4 sections, the no. of workers in the different sections being 50,
100, 60 and 150. The average wages per worker are 100, 120, 130 and
110 respectively, calculate the average wages for all the workers together.
[Ans: 102.22]
Answers
Answer:
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