The NCERT Solutions for Class 11 Maths Chapter 13 Statistics Exercise 13.1 cover every question on mean deviation, 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.
Exercise 13.1 is the first exercise on measures of dispersion, and it teaches students how to find mean deviation. The exercise has 12 questions built around these skills:
- Finding mean deviation about the mean for raw data and frequency data.
- Finding mean deviation about the median after arranging the data.
- Handling discrete and continuous frequency distributions with a table.
Topics Covered in Exercise 13.1
This exercise introduces dispersion, which measures how spread out a set of values is. Two averages tell the same story only when the spread is known. Exercise 13.1 keeps the focus on one measure of spread, the mean deviation, which is the average of the absolute distances of each value from a central point.
- Mean deviation about the mean: average of |xi − x̄| over all values.
- Mean deviation about the median: average of |xi − M| after the data is sorted.
- Ungrouped (raw) data: a plain list of numbers, as in Questions 1 to 4.
- Discrete frequency data: each value xi has a frequency fi, as in Questions 5 to 8.
- Continuous frequency data: class intervals with mid-points, as in Questions 9 to 12.
Important: mean deviation always uses the absolute value, so every distance is counted as positive. Dropping the modulus is the single biggest error in this exercise.
Question-wise Breakdown of Exercise 13.1
The NCERT Solutions for Class 11 Maths Chapter 13 Statistics Exercise 13.1 solve all 12 questions in order. The table below shows what each block of questions asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Question | What it asks | Skill tested |
|---|---|---|
| Q1–Q2 | Mean deviation about the mean for raw data | Basic definition |
| Q3–Q4 | Mean deviation about the median for raw data | Sorting, then median |
| Q5–Q6 | Mean deviation about the mean, discrete frequency | Using fixi tables |
| Q7–Q8 | Mean deviation about the median, discrete frequency | Cumulative frequency |
| Q9–Q10 | Mean deviation about the mean, continuous data | Class mid-points |
| Q11–Q12 | Mean deviation about the median, continuous data | Median class formula |
Most questions ask students to build a table first, so neat column work saves time and prevents slips in the totals.
Key Formulas and Definitions for Exercise 13.1
Exercise 13.1 rests on a small set of formulas for mean deviation. Students should write these at the top of their rough work before starting any question.
| Quantity | Formula |
|---|---|
| Mean of raw data | x̄ = (Σ xi) / n |
| M.D. about mean (raw) | M.D.(x̄) = (1/n) Σ |xi − x̄| |
| M.D. about median (raw) | M.D.(M) = (1/n) Σ |xi − M| |
| Mean of frequency data | x̄ = (Σ fixi) / N, where N = Σ fi |
| M.D. about mean (frequency) | M.D.(x̄) = (1/N) Σ fi |xi − x̄| |
| Median (continuous) | M = l + [(N/2 − cf) / f] × h |
Tip: for the median, always sort raw data first. If the number of values is even, the median is the average of the two middle terms.
Common Mistakes in Exercise 13.1
Students lose easy marks in Exercise 13.1 on small slips inside the table. The list below covers the errors that show up most often in class tests on the NCERT Solutions for Class 11 Maths Chapter 13 Statistics Exercise 13.1.
- Dropping the modulus and letting distances cancel out. Every |xi − x̄| must be positive.
- Using the mean when the question asks for deviation about the median, or the reverse.
- Forgetting to sort the data before reading off the median.
- Taking N as the number of classes instead of N = Σ fi in frequency questions.
Practice Questions for Exercise 13.1
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 Exercise 13.1.
Practice Card: Solved Practice Questions for Class 11 Maths Statistics Exercise 13.1 — attempt each question, then check the worked solution.
Other Exercises of Chapter 13 Statistics
Chapter 13 Statistics has two exercises plus a Miscellaneous Exercise. Use the table to move to the next exercise once Exercise 13.1 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 13.2 | Class 11 Maths Statistics Exercise 13.2 Solutions |
| Miscellaneous Exercise | Class 11 Maths Statistics Miscellaneous Exercise 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 11,210 Class 11 students conducted before the 2026 exams, 64% of students said the continuous-data questions (Q9 to Q12) in Exercise 13.1 took them the longest, while the raw-data mean deviation questions were rated the easiest to score.
FAQs on NCERT Solutions for Class 11 Maths Chapter 13 Statistics Exercise 13.1
Statistics NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 13 Statistics Exercise 13.1?
Ans. Exercise 13.1 has 12 questions on mean deviation. Questions 1 to 4 use raw data, Questions 5 to 8 use discrete frequency data, and Questions 9 to 12 use continuous frequency distributions. Some ask for deviation about the mean and others about the median.
Ques. What is mean deviation in Class 11 Maths Statistics?
Ans. Mean deviation is a measure of dispersion. It is found by taking the average of |xi − a|, where a is either the mean or the median. Because it uses the absolute value, every distance is counted as positive, so the spread is never zero for varied data.
Ques. What is the difference between mean deviation about the mean and about the median?
Ans. Mean deviation about the mean uses M.D.(x̄) = (1/n) Σ |xi − x̄|, so distances are measured from the average. Mean deviation about the median uses the middle value M instead. The data must be sorted before the median can be read off.
Ques. Why do we take the absolute value in mean deviation?
Ans. The sum of the plain deviations from the mean is always zero, so it cannot measure spread. Taking the absolute value keeps every distance positive, which gives a true picture of how far the values lie from the centre. This is the core idea tested in Exercise 13.1.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 13 Statistics Exercise 13.1 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 13 Statistics Exercise 13.1 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.
Comments