RD Sharma Solutions for Class 11 Chapter 32 - Statistics Exercise 32.7

In this section, we shall see how we can use various measures of dispersion to compare two or more series. The solutions prepared by our expert faculty team help students in their exam preparation to secure full marks in Maths. The Solutions given in this page contains detailed step-by-step explanations to all the problems that come under this chapter. These solutions will help you in gaining knowledge and strong command over the subject. If you wish to secure an excellent score, solving RD Sharma Class 11 Maths Solutions is a must. Here is the RD Sharma Solutions for Class 11 Chapter 32 where solutions are solved in detail. Students can download the pdf of this chapter, in their respective links.

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Also, access other exercises of RD Sharma Solutions for Class 11 Maths Chapter 32 – Statistics

Exercise 32.1 Solutions

Exercise 32.2 Solutions

Exercise 32.3 Solutions

Exercise 32.4 Solutions

Exercise 32.5 Solutions

Exercise 32.6 Solutions

Access answers to RD Sharma Solutions for Class 11 Maths Exercise 32.7 Chapter 32 – Statistics

EXERCISE 32.7 PAGE NO: 32.47

1. Two plants A and B of a factory show the 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

₹2500

₹2500

The variance of distribution of wages

81

100

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

Solution:

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 more variability in salary.

∴ Plant B has more variability in individual wages than plant A

2. The means and standard deviations of heights and weights of 50 students in a class are as follows:

Weights

Heights

Mean

63.2 kg

63.2 inch

Standard deviation

5.6 kg

11.5 inch

Which shows more variability, heights or weights?

Solution:

RD Sharma Solutions for Class 11 Maths Chapter 32 – Statistics - image 96

3. The coefficient of variation of two distribution are 60% and 70%, and their standard deviations are 21 and 16 respectively. What is their arithmetic means?

Solution:

RD Sharma Solutions for Class 11 Maths Chapter 32 – Statistics - image 97

= 22.86

∴ Means are 35 and 22.86

4. Calculate coefficient 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

Solution:

RD Sharma Solutions for Class 11 Maths Chapter 32 – Statistics - image 98

RD Sharma Solutions for Class 11 Maths Chapter 32 – Statistics - image 99

5. An analysis of the weekly 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

Average weekly wages

₹52.5

₹47.5

The variance of the distribution of wages

100

121


(i) Which firm A or B pays out the larger amount as weekly wages?
(ii) Which firm A or B has greater variability in individual wages?

Solution:

RD Sharma Solutions for Class 11 Maths Chapter 32 – Statistics - image 100

6. The following are some particulars of the distribution of weights of boys and girls in a class:

Boys

Girls

Number

100

50

Mean weight

60 kg

45 kg

Variance

9

4


Which of the distributions is more variable?

Solution:

RD Sharma Solutions for Class 11 Maths Chapter 32 – Statistics - image 101

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