NCERT Solutions for Class 11 Maths Chapter 13

NCERT solutions for Class 11 Maths Chapter 13 Statistics – complete answers & explanations

Class 11 Mathematics Chapter 13 Statistics is an important chapter that helps students understand how numerical data can be analysed using mathematical methods. In this chapter, students learn how to calculate mean deviation, variance, and standard deviation for both grouped and ungrouped data. These concepts are widely used in higher mathematics and in real-life situations where data needs to be interpreted carefully. A clear understanding of statistics improves logical thinking and accuracy in calculations. This blog provides clear and reliable NCERT solutions that help students follow the correct approach to answering questions step by step. Parents and teachers can also use these answers to support students during revision and homework. Download the worksheet and practice alongside solutions for better clarity. Book a free trial now to get expert guidance.

What this NCERT chapter covers?

1. This chapter explains how to measure variation in data using mean deviation about the mean and median. 
2. Students learn how to organise data into tables using frequency and cumulative frequency. 
3. It introduces important statistical concepts such as variance and standard deviation. 
4. The chapter teaches students how to apply formulas to grouped and ungrouped data sets. 
5. Learners understand how to interpret data through calculations and numerical reasoning. 
6. It helps students develop problem-solving skills by working with real-life data examples such as marks, height, and income tables. 
7. Students practise calculating central tendency and dispersion values accurately. 
8. The chapter strengthens mathematical reasoning required for exams and higher-level mathematics. 
9. It improves numerical accuracy and careful step-by-step calculation skills. 
10. Understanding this chapter helps students perform better in school assessments and competitive examinations.

How to use these NCERT solutions?

1. Students should first read the question carefully and attempt to solve it independently. 
2. After solving, they can compare their steps with the answers provided to check accuracy. 
3. If mistakes occur, students should identify the step where the calculation went wrong. 
4. Parents and teachers can use these solutions to guide students during practice sessions. 
5. These solutions follow the same sequence as the worksheet, making revision easier. 
6. Students can use the answers to understand the correct method of applying formulas. 
7. Regular practice with these solutions helps build confidence before examinations. 
8. Teachers can also use these answers for quick verification and classroom discussion.

Important tips & tricks for students

1. Always write the formula before starting any statistical calculation. 
2. Arrange numerical data properly before finding the median or mean. 
3. Double-check arithmetic calculations to avoid small numerical errors. 
4. Pay attention to units such as cm, mm, or numbers while solving problems. 
5. Carefully calculate cumulative frequency before determining the median class. 
6. Do not skip steps while calculating variance or standard deviation. 
7. Practise solving tables regularly to improve speed and accuracy. 
8. Read each question completely before starting calculations. 
9. Keep your work neat and organised to reduce mistakes. 
10. Revise formulas frequently to remember them during exams.

NCERT solutions – complete answer key

Exercise 13.1

Question 1 
Answer: 3 

Question 2 
Answer: 8.4 

Question 3 
Answer: 2.33 

Question 4 
Answer: 7 

Question 5 
Answer: 6.32 

Question 6 
Answer: 16 

Question 7 
Answer: 3.23 

Question 8 
Answer: 5.10 

Question 9 
Answer: 157.92 

Question 10 
Answer: 11.29 

Question 11 
Answer: 10.34 

Question 12 
Answer: 7.35 

Exercise 13.2

Question 1 
Answer: Mean = 9, Variance = 9.25 

Question 2 
Answer: Mean = (n + 1)/2, Variance = (n² – 1)/12 

Question 3 
Answer: Mean = 16.5, Variance = 74.25 

Question 4 
Answer: Mean = 19, Variance = 43.4 

Question 5 
Answer: Mean = 100, Variance = 29.09 

Question 6 
Answer: Mean = 64, Standard deviation = 1.69 

Question 7 
Answer: Mean = 107, Variance = 2276 

Question 8 
Answer: Mean = 27, Variance = 132 

Question 9 
Answer: Mean = 93, Variance = 105.58, Standard deviation = 10.28 

Question 10 
Answer: Mean diameter = 43.5 mm, Standard deviation = 5.55 mm 

Miscellaneous exercise

Question 1 
Answer: Remaining observations = 6 + √47 and 6 – √47 

Question 2 
Answer: The remaining two observations are 6 and 8 

Question 3 
Answer: New mean = 24 
Answer: New standard deviation = 12 

Question 4 
Answer: Mean = ax̄ 
Answer: Variance = a²σ² 

Question 5 

Part (i) 
Answer: Correct mean = 10.11 
Answer: Correct standard deviation = 2.71 

Part (ii) 
Answer: Correct mean = 10.2 
Answer: Correct standard deviation = 1.99 

Question 6 
Answer: New mean = 20 
Answer: New standard deviation = 3.04

Why NCERT solutions help students?

NCERT solutions help students understand the correct method of solving questions and build strong conceptual clarity. They improve exam readiness by providing structured answers that match curriculum expectations. Regular practice with NCERT-aligned answers increases confidence and helps students perform better in assessments.

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