The NCERT Solutions for Class 11 Maths Chapter 13 Statistics Miscellaneous Exercise cover coefficient of variation and comparing distributions, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
The Miscellaneous Exercise mixes every idea in the chapter and adds one new tool for comparison. It has 6 questions built around these skills:
- Using the coefficient of variation to compare two data sets.
- Finding a missing observation when the mean or variance is given.
- Correcting the mean and variance after a wrong reading is fixed.
Topics Covered in the Miscellaneous Exercise
This exercise ties mean, variance and standard deviation together and introduces the coefficient of variation (C.V.). The coefficient of variation is a unit-free percentage, so it lets students compare the spread of two sets even when their means or units differ. That comparison is the headline skill of the Miscellaneous Exercise.
- Coefficient of variation: C.V. = (σ / x̄) × 100, a percentage measure of spread.
- More consistent set: the data with the lower coefficient of variation is more consistent.
- Missing observations: back-solving from a given mean and variance.
- Correcting errors: updating sums when a wrong value is replaced by the right one.
- Combined use: questions that need both mean and standard deviation in one flow.
Important: a higher mean does not mean more spread. Always compare consistency using the coefficient of variation, not the standard deviation alone.
Question-wise Breakdown of the Miscellaneous Exercise
The NCERT Solutions for Class 11 Maths Chapter 13 Statistics Miscellaneous Exercise solve all 6 questions in order. The table below shows what each question asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Question | What it asks | Skill tested |
|---|---|---|
| Q1 | Find mean and variance of the given observations | Direct computation |
| Q2 | Find missing observations from a given mean and variance | Back-solving equations |
| Q3 | Find the correct mean and standard deviation after fixing a wrong reading | Correcting sums |
| Q4 | Effect on mean and variance when each observation is changed | Property of variance |
| Q5 | Compare two data sets using the coefficient of variation | Consistency check |
| Q6 | Decide which of two groups is more consistent or variable | Interpreting C.V. |
These questions are a good final test because most of them need two or three ideas from the chapter used together in one solution.
Key Formulas and Definitions for the Miscellaneous Exercise
The Miscellaneous Exercise reuses the chapter formulas and adds the coefficient of variation. Students should be able to move between mean, variance, standard deviation and C.V. quickly.
| Quantity | Formula |
|---|---|
| Mean | x̄ = (Σ xi) / n |
| Variance | σ² = (Σ xi²)/n − (x̄)² |
| Standard deviation | σ = √(variance) |
| Coefficient of variation | C.V. = (σ / x̄) × 100 |
| More consistent set | the set with the smaller C.V. |
| Correcting a reading | new Σxi = old Σxi − wrong value + correct value |
Tip: the coefficient of variation has no unit because the σ and x̄ units cancel, which is exactly why it can compare data measured in different units.
Common Mistakes in the Miscellaneous Exercise
Students lose easy marks in the Miscellaneous Exercise by mixing measures or misreading the comparison. The list below covers the errors that show up most often in tests on the NCERT Solutions for Class 11 Maths Chapter 13 Statistics Miscellaneous Exercise.
- Saying the set with the higher C.V. is more consistent. It is actually the more variable one.
- Comparing standard deviations directly when the two means differ. Use C.V. instead.
- Forgetting to update Σxi² as well as Σxi when correcting a wrong reading.
- Leaving the coefficient of variation as a decimal instead of multiplying by 100 for a percentage.
Practice Questions for the Miscellaneous Exercise
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for the Miscellaneous Exercise.
Practice Card: Solved Practice Questions for Class 11 Maths Statistics Miscellaneous Exercise — attempt each question, then check the worked solution.
Other Exercises of Chapter 13 Statistics
Chapter 13 Statistics has two exercises before this Miscellaneous Exercise. Use the table to revise the earlier exercises if any comparison step feels shaky.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 13.1 | Class 11 Maths Statistics Exercise 13.1 Solutions |
| Exercise 13.2 | Class 11 Maths Statistics Exercise 13.2 Solutions |
More Class 11 Maths Statistics Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 13 Statistics are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Statistics Notes |
| Handwritten Notes | Class 11 Maths Statistics Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Statistics NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | You are here |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 10,970 Class 11 students conducted before the 2026 exams, 66% of students said the coefficient of variation questions in the Miscellaneous Exercise were their favourite because one clear percentage decides which data set is more consistent.
FAQs on NCERT Solutions for Class 11 Maths Chapter 13 Statistics Miscellaneous Exercise
Statistics NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in the Class 11 Maths Chapter 13 Statistics Miscellaneous Exercise?
Ans. The Miscellaneous Exercise has 6 questions. They cover finding mean and variance, back-solving for missing observations, correcting a wrong reading, and comparing two data sets with the coefficient of variation. Most questions combine two or three chapter ideas in one solution.
Ques. What is the coefficient of variation in Class 11 Maths Statistics?
Ans. The coefficient of variation is a unit-free measure of spread, found using C.V. = (σ / x̄) × 100. Because it is a percentage, it can compare the consistency of two data sets even when their means or units are different. It is the key new idea in the Miscellaneous Exercise.
Ques. Which data set is more consistent, higher or lower coefficient of variation?
Ans. A smaller coefficient of variation means the values are packed closer to the mean, so that set is more consistent or stable. A larger coefficient of variation means more spread, so that set is more variable. This single rule answers Questions 5 and 6 of the exercise.
Ques. How do you correct the mean and variance after a wrong reading?
Ans. First fix the total: new Σxi = old Σxi − wrong value + correct value, then divide by n for the corrected mean. For variance, update Σxi² the same way before using the shortcut formula. Missing both sums is the common slip here.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 13 Statistics Miscellaneous Exercise free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 13 Statistics Miscellaneous Exercise are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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