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 help students in their exam preparation to secure full marks in Maths. The Solutions given on this page contain detailed step-by-step explanations of 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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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:
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:
= 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:
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:
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:
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