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Two Plants A And B of a Factory Show Following Results About the Number of Workers and the Wages Paid to Them in Which Plant A Or B Is There Greater Variability in Individual Wages?

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Question

Two plants A and B of a factory show following results about the number of workers and the wages paid to them 

  Plant A Plant B
No. of workers 5000 6000
Average monthly wages Rs 2500 Rs 2500
Variance of distribution of wages 81 100

In which plant A or B is there greater variability in individual wages?

 

 

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Solution

Variance of the distribution of wages in plant

\[A\left( \sigma^2 \right) = 81\]
Standard deviation of the distribution of wages in plant 
\[A\left( \sigma \right) = 9\]
Variance of the distribution of wages in plant 
\[B\left( \sigma^2 \right) = 100\] 
Standard deviation of the distribution of wages in plant 
\[B\left( \sigma \right) = 10\]
Average monthly wages in both the plants are Rs 2500.
Thus, the plant with greater value of SD will have more variability in salary.
Plant B has more variability in individual wages than plant A.
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Chapter 32: Statistics - Exercise 32.7 [Page 47]

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R.D. Sharma Mathematics [English] Class 11
Chapter 32 Statistics
Exercise 32.7 | Q 1 | Page 47

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