The Total solution for NCERT class 6-12
Two plants A and Bof a factory show the following results about the number of workers and thewages paid to them
Plant A
Plant B
No. of workers
5000
6000
Average monthly wages
₹2500
The variance of distribution of wages
81
100
In which plant A orB is there greater variability in individual wages?
Answer - 1 : -
Variation of the distribution of wages in plant A (σ2 =18)
So, Standard deviation of the distribution A (σ – 9)
Similarly, the Variation of the distribution of wages in plant B (σ2 =100)
So, Standard deviation of the distribution B (σ – 10)
And, Average monthly wages in both the plants is 2500,
Since, the plant with a greater value of SD will have morevariability in salary.
∴ PlantB has more variability in individual wages than plant A
The means andstandard deviations of heights and weights of 50 students in a class are asfollows:
Weights
Heights
Mean
63.2 kg
63.2 inch
Standard deviation
5.6 kg
11.5 inch
Which shows morevariability, heights or weights?
Answer - 2 : -
The coefficient ofvariation of two distribution are 60% and 70%, and their standard deviationsare 21 and 16 respectively. What is their arithmetic means?
Answer - 3 : -
= 22.86
∴ Meansare 35 and 22.86
Calculatecoefficient of variation from the following data:
Income (in ₹):
1000-1700
1700-2400
2400-3100
3100-3800
3800-4500
4500-5200
No. of families:
12
18
20
25
35
10
Answer - 4 : -
An analysis of theweekly wages paid to workers in two firms A and B, belonging to the sameindustry gives the following results:
Firm A
Firm B
No. of wage earners
586
648
Average weekly wages
₹52.5
₹47.5
The variance of the distribution of wages
121
(i) Which firm A or B pays out the larger amount asweekly wages?(ii) Which firm A or B has greater variability inindividual wages?
Answer - 5 : -
The following aresome particulars of the distribution of weights of boys and girls in a class:
Boys
Girls
Number
50
Mean weight
60 kg
45 kg
Variance
9
4
Which of the distributions is more variable?
Answer - 6 : -