Learn
Class 10 Statistics: 8 practice questions with answers, step by step
These are 8 practice questions on NCERT Class 10 Maths Chapter 13, Statistics, each with a worked answer. They cover the mean, median and mode: first for a short list of numbers, then for grouped data using class marks and the textbook's formulas. Try each one on paper before you open the answer. The Class 9 side of this idea, averages of groups of different sizes, is in the Class 9 Understanding Data questions.
These questions are our own, drafted with AI help. Every answer was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.
What the chapter says you need
Facts from the NCERT textbook (Mathematics, Textbook for Class X, Reprint 2026-27, Chapter 13, printed pages 171 to 201):
- The mean of observations is the sum of the values divided by the number of observations (section 13.2, page 171).
- For grouped data, each class is represented by its class mark, the average of its lower and upper limits (page 173). The direct method mean is x̄ = Σfᵢxᵢ ÷ Σfᵢ (summary, page 200).
- Mode of grouped data: the modal class is the class with the maximum frequency, and Mode = l + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h, where l is the lower limit of the modal class, h the class size, f₁ its frequency, f₀ the frequency of the class before it and f₂ the frequency of the class after it (section 13.3, page 184; summary, page 201).
- Median of ungrouped data: arrange the values in ascending order; if n is odd the median is the ((n + 1)/2)th observation, and if n is even it is the average of the (n/2)th and the (n/2 + 1)th observations (section 13.4, page 188).
- Median of grouped data: find the median class, the class whose cumulative frequency is greater than (and nearest to) n/2 (page 193). Then Median = l + [(n/2 − cf) ÷ f] × h, where cf is the cumulative frequency of the class before it, f its frequency and h the class size (page 193; summary, page 201).
Mean, median and class marks
Question 1. Find the mean of 5, 8, 12, 15 and 20.
Answer: 12. Sum = 5 + 8 + 12 + 15 + 20 = 60; mean = 60 ÷ 5 = 12.
Question 2. The mean of 6 numbers is 15. One of them, 20, is removed. What is the mean of the other 5?
Answer: 14. Total = 6 × 15 = 90. Without 20 the total is 70, and 70 ÷ 5 = 14.
Question 3. Find the median of 3, 7, 9, 12, 15, 18.
Answer: 10.5. The values are already in order and n = 6 is even, so the median is the average of the 3rd and 4th values: (9 + 12) ÷ 2 = 10.5. (Page 188.)
Question 4. What is the class mark of the class interval 20–30?
Answer: 25. Class mark = (lower limit + upper limit) ÷ 2 = (20 + 30) ÷ 2 = 25. (Page 173.)
Grouped data
Question 5. Find the mean of this grouped data using class marks: class 0–10 has frequency 4, 10–20 has 6, 20–30 has 6 and 30–40 has 4.
Answer: 20. The class marks are 5, 15, 25 and 35. Σfx = 5 × 4 + 15 × 6 + 25 × 6 + 35 × 4 = 20 + 90 + 150 + 140 = 400, and Σf = 4 + 6 + 6 + 4 = 20. Mean = 400 ÷ 20 = 20. (Direct method, page 200.)
Question 6. In a grouped frequency distribution with class size 10, the modal class is 20–30. Its frequency is 12, the class before it has frequency 8, and the class after it has frequency 6. Find the mode.
Answer: 24. l = 20, h = 10, f₁ = 12, f₀ = 8, f₂ = 6. Mode = 20 + [(12 − 8) ÷ (2 × 12 − 8 − 6)] × 10 = 20 + (4 ÷ 10) × 10 = 20 + 4 = 24. (Page 184.)
Question 7. A class has these frequencies: 0–10 has 5, 10–20 has 8, 20–30 has 12, 30–40 has 10 and 40–50 has 5. Find the mean by the direct method.
Answer: 25.5. Class marks 5, 15, 25, 35, 45. Σfx = 5 × 5 + 15 × 8 + 25 × 12 + 35 × 10 + 45 × 5 = 25 + 120 + 300 + 350 + 225 = 1,020. Σf = 5 + 8 + 12 + 10 + 5 = 40. Mean = 1,020 ÷ 40 = 25.5. (Page 200.)
Question 8. For the same data as question 7, find the median.
Answer: about 25.83. The cumulative frequencies are 5, 13, 25, 35, 40, and n = 40, so n/2 = 20. The class whose cumulative frequency (25) is greater than and nearest to 20 is 20–30, so the median class is 20–30. Then l = 20, cf = 13, f = 12, h = 10: Median = 20 + [(20 − 13) ÷ 12] × 10 = 20 + 70/12 ≈ 20 + 5.83 = 25.83. (Page 193.)
Practise more, and check your marks
- Free practice, marked instantly in your browser: Class 10 Statistics questions. Questions 1 to 6 above are all in this set.
- Printable worksheets with answer keys, in English, Hindi and Marathi: Class 10 worksheets.
- See which unit this chapter belongs to and how CBSE splits the 80 theory marks in our Class 10 Maths syllabus 2026-27 guide.
- The same step-by-step style for another chapter: Class 10 Real Numbers.
Where CMDLearn fits
CMDLearn is building an AI tutor for Classes 1 to 10 that explains a step and checks the child's working, but leaves the writing to the child. It is still in development, and no child uses it yet. If you would like to hear when there is something to try, you can join the waitlist.
Sources
All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook.
- NCERT, Mathematics, Textbook for Class X, Chapter 13 "Statistics" (Reprint 2026-27), printed pages 171-201 (the mean, section 13.2, page 171; the class mark, page 173; the mode of grouped data, section 13.3, page 184; the median of ungrouped data, section 13.4, page 188; the median of grouped data, page 193; the summary formulas, pages 200-201): ncert.nic.in/textbook/pdf/jemh113.pdf
The definitions and formulas are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the official CBSE notices.