NCERT Solutions for Class 11 Maths Chapter 13 Statistics

This worksheet provides complete and accurate NCERT Solutions for Class 11 Mathematics Chapter 13 Statistics. In this chapter, students learn how to calculate and interpret statistical measures such as mean deviation, variance, and standard deviation using different methods. The chapter helps students understand how numerical data can be organised and analysed in a structured way. Statistics is an important topic because it builds analytical thinking and problem-solving skills that are useful in higher mathematics and real-life data interpretation. This worksheet follows the exact NCERT structure and provides reliable step-by-step answers that support students during homework, revision, and exam preparation.

Chapter summary: stories, poems & themes

This chapter is concept-based and focuses on numerical data analysis rather than stories or poems. Students learn how to work with grouped and ungrouped data using statistical formulas and calculations. The chapter mainly includes problem-solving activities involving tables, numerical values, and mathematical reasoning. The learning focus is on understanding statistical measures and applying formulas correctly to obtain accurate results. The chapter is calculation-based and requires careful observation of numerical data.

What this NCERT chapter covers?

• Calculation of mean deviation about the mean and median 
• Understanding cumulative frequency and median calculation 
• Learning variance and standard deviation concepts 
• Working with grouped and ungrouped data tables 
• Applying statistical formulas to real-life data sets 
• Improving logical reasoning and numerical accuracy 

How to use these NCERT solutions?

Students should first attempt each question before checking the answers in this worksheet. Parents and teachers can use these solutions to verify correctness and guide students step by step. The answers follow the same order and structure as the NCERT textbook, making revision easier and more organised.

Student tips & learning tricks

• Always arrange data in ascending order before finding the median 
• Carefully calculate cumulative frequencies for grouped data 
• Double-check calculations while finding mean deviation and variance 
• Write formulas clearly before starting calculations 
• Avoid skipping steps during calculations 

Why NCERT solutions are important?

NCERT-aligned solutions help students learn the correct method of solving mathematical problems according to curriculum standards. Strong foundational learning in statistics improves accuracy, confidence, and exam readiness.

Complete answer key – NCERT solutions

Exercise 13.1

Question 1 
Mean deviation about the mean for 4, 7, 8, 9, 10, 12, 13, 17 

Answer: 3 


Question 2 
Mean deviation about the mean for 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 

Answer: 8.4 


Question 3 
Mean deviation about the median for 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17 

Answer: 2.33 


Question 4 
Mean deviation about the median for 36, 72, 46, 42, 60, 45, 53, 46, 51, 49 

Answer: 7 


Question 5 
Mean deviation about the mean 

Answer: 6.32 


Question 6 
Mean deviation about the mean 

Answer: 16 


Question 7 
Mean deviation about the median 

Answer: 3.23 


Question 8 
Mean deviation about the median 

Answer: 5.10 


Question 9 
Mean deviation about the mean 

Answer: 157.92 


Question 10 
Mean deviation about the mean 

Answer: 11.29 


Question 11 
Mean deviation about the median 

Answer: 10.34 


Question 12 
Mean deviation about median age 

Answer: 7.35 

Exercise 13.2

Question 1 
Mean = 9 
Variance = 9.25 


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


Question 3 
Mean = 16.5 
Variance = 74.25 


Question 4 
Mean = 19 
Variance = 43.4 


Question 5 
Mean = 100 
Variance = 29.09 


Question 6 
Mean = 64 
Standard deviation = 1.69 


Question 7 
Mean = 107 
Variance = 2276 


Question 8 
Mean = 27 
Variance = 132 


Question 9 
Mean = 93 
Variance = 105.58 
Standard deviation = 10.28 


Question 10 
Mean diameter = 43.5 mm 
Standard deviation = 5.55 mm 

Miscellaneous exercise

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


Question 2 
Remaining observations = 6 and 8 


Question 3 
New mean = 24 
New standard deviation = 12 


Question 4 
Mean = ax̄ 
Variance = a²σ² 


Question 5 

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

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


Question 6 
New mean = 20 
New standard deviation = 3.04 


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