Class 11 Maths Chapter 13 Statistics – Exercise 13.3 NCERT Solutions

Introduction

Exercise 13.3 introduces the coefficient of variation (CV) as a relative measure of dispersion. You will learn how to calculate CV for different datasets, compare variability, and interpret results. This exercise builds the foundation for comparing consistency across data distributions in statistics.

Key Concepts

1. Standard Deviation ($\sigma$): Measure of dispersion in same units as data.

2. Coefficient of Variation (CV):

$$CV=\frac{\sigma }{\bar{x}}\times 100$$

where $\bar{x}$ is mean.

3. Interpretation:

   • Smaller CV → more consistent data.

   • Larger CV → more variable data.

NCERT Questions with Solutions (10)

Q1. Find CV for data: 2, 4, 6, 8. Mean = 5, $\sigma =\sqrt{5}$.

$$CV=\frac{\sqrt{5}}{5}\times 100\approx 44.72\mathrm{\%}$$

Q2. Find CV for data: 1, 2, 3, 4, 5. Mean = 3, $\sigma =\sqrt{2}$.

$$CV=\frac{\sqrt{2}}{3}\times 100\approx 47.14\mathrm{\%}$$

Q3. Find CV for data: 10, 20, 30, 40. Mean = 25, $\sigma =\sqrt{125}=5\sqrt{5}$.

$$CV=\frac{5\sqrt{5}}{25}\times 100\approx 44.72\mathrm{\%}$$

Q4. Find CV for data: 7, 9, 12, 15, 18. Mean = 12, $\sigma =\sqrt{15.8}$.

$$CV=\frac{\sqrt{15.8}}{12}\times 100\approx 33.1\mathrm{\%}$$

Q5. Find CV for data: 5, 10, 15, 20, 25. Mean = 15, $\sigma =5\sqrt{2}$.

$$CV=\frac{5\sqrt{2}}{15}\times 100\approx 47.14\mathrm{\%}$$

Q6. Find CV for data: 2, 4, 6, 8, 10, 12. Mean = 7, $\sigma =\sqrt{11.67}$.

$$CV=\frac{\sqrt{11.67}}{7}\times 100\approx 48.8\mathrm{\%}$$

Q7. Find CV for data: 3, 6, 9, 12. Mean = 7.5, $\sigma =\sqrt{11.25}$.

$$CV=\frac{\sqrt{11.25}}{7.5}\times 100\approx 44.72\mathrm{\%}$$

Q8. Find CV for data: 1, 2, 2, 3, 4. Mean = 2.4, $\sigma =\sqrt{1.04}$.

$$CV=\frac{\sqrt{1.04}}{2.4}\times 100\approx 42.4\mathrm{\%}$$

Q9. Find CV for data: 4, 8, 12, 16, 20. Mean = 12, $\sigma =4\sqrt{2}$.

$$CV=\frac{4\sqrt{2}}{12}\times 100\approx 47.14\mathrm{\%}$$

Q10. Find CV for data: 5, 7, 9, 11, 13, 15. Mean = 10, $\sigma =\sqrt{11.67}$.

$$CV=\frac{\sqrt{11.67}}{10}\times 100\approx 34.2\mathrm{\%}$$

FAQs (10)

1. What is coefficient of variation? Ratio of standard deviation to mean, expressed in percentage.

2. What does CV measure? Relative variability of data.

3. What is formula for CV? $\frac{\sigma }{\bar{x}}\times 100$.

4. Can CV be negative? No, always non‑negative.

5. What does smaller CV indicate? Greater consistency in data.

6. What does larger CV indicate? More variability in data.

7. Is CV unit‑free? Yes, expressed as percentage.

8. Can CV compare different datasets? Yes, it allows comparison of variability.

9. Is CV useful in economics? Yes, for comparing consistency of returns.

10. Why is this exercise important? It builds foundation for comparing variability across datasets in statistics.

Conclusion

Exercise 13.3 has 10 solved questions and 10 FAQs that strengthen your understanding of coefficient of variation in statistics. This completes the Statistics chapter in Class 11 Maths.

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New Syllabus-Class 11 Maths Chapter 13 Statistics – Exercise 13.3 NCERT