CBSE Class 10 Mathematics (Standard) Chapter 13 Statistics Important Questions 2027
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25 questions from Statistics appeared in 7 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Statistics & Probability unit — 11 marks in the official syllabus
- Asked in 7 of 7 analysed papers (2022–2026)
- About 3.6 questions per paper (OR alternatives counted separately)
- 8 question patterns repeated across papers
Important topics in Statistics
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Empirical relationship / mixed central tendency problems | Board 2023Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| 2 | Median of grouped data | Board 2022Board 2023Board 2024Sample 2025 | ★★☆☆☆ |
| 3 | Mean of grouped data (direct / assumed mean / step deviation) | Board 2022Board 2023Board 2024Sample 2025 | ★☆☆☆☆ |
| 4 | Mode of grouped data | Board 2022Board 2023Board 2024 | ★☆☆☆☆ |
Repeated questions from Statistics
1. Missing frequency from one measure, then compute another
2×Board 2025Sample 20265 marks
If the mode of the following distribution is 55, then find the value of x. Hence, find the mean. Class Interval: 0-15, 15-30, 30-45, 45-60, 60-75, 75-90; Frequency: 10, 7, x, 15, 10, 12
2. Effect of adding a constant to every observation
2×Board 2023Sample 20261 marks
The median of a set of 9 distinct observations is 20.5. If each of the observations of the set is increased by 2, then the median of the new set (A) is increased by 2 (B) is decreased by 2 (C) is two times the original number (D) Remains same as that of original observations
3. Definition of median
2×Board 2024Sample 20251 marks
Which of the following gives the middle most observation of the data? A) Median B) Mean C) Range D) Mode
4. Identify the median class
2×Board 2024Sample 20251 marks
Consider the frequency distribution of 45 observations. Class: 0-10, 10-20, 20-30, 30-40, 40-50; Frequency: 5, 9, 15, 10, 6. The upper limit of median class is A) 20 B) 10 C) 30 D) 40
5. Empirical formula: third measure from other two
2×Board 2025Board 20261 marks
The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is : (A) 43.4 (B) 42.4 (C) 44.2 (D) 49.3
6. Median of a grouped frequency table
2×Board 2023Board 20242 marks
[case context: BINGO game with 75 numbered balls; grouped frequency table of 48 announced numbers in classes 0-15(8), 15-30(9), 30-45(10), 45-60(12), 60-75(9).] Find median of the given data.
7. Mode of a grouped frequency table
2×Board 2022Board 20242 marks
[case context: BINGO game with 75 numbered balls; grouped frequency table of 48 announced numbers in classes 0-15(8), 15-30(9), 30-45(10), 45-60(12), 60-75(9).] Find mode of the given data.
8. Mean of a grouped frequency table
2×Board 2022Board 20232/3 marks
[case context: IMD table of sub-division wise monsoon rainfall (mm) in 2018 - classes 200-400 to 1600-1800 with frequencies 2,4,7,4,2,3,1,1] Find the mean rainfall in this season.
Statistics questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 3 | 8 |
| Board 2023 | 6 | 8 |
| Board 2024 | 5 | 7 |
| Board 2025 | 2 | 6 |
| Sample 2025 | 4 | 12 |
| Board 2026 | 2 | 6 |
| Sample 2026 | 3 | 11 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Statistics
Board 2026 2 questions
The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is : (A) 43.4 (B) 42.4 (C) 44.2 (D) 49.3
An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. The health insurance policies are given to persons of age 15 years and onwards, but less than 60 years. Age (in yrs) / Number of policy holders: 15-20: 2, 20-25: 4, 25-30: 18, 30-35: 21, 35-40: 33, 40-45: 11, 45-50: 3, 50-55: 6, 55-60: 2. Find the modal age and median age of the policy holders.
Sample 2026 3 questions
The median of a set of 9 distinct observations is 20.5. If each of the observations of the set is increased by 2, then the median of the new set (A) is increased by 2 (B) is decreased by 2 (C) is two times the original number (D) Remains same as that of original observations
If the mode of the following distribution is 55, then find the value of x. Hence, find the mean. Class Interval: 0-15, 15-30, 30-45, 45-60, 60-75, 75-90; Frequency: 10, 7, x, 15, 10, 12
A survey regarding heights (in cm) of 51 girls of class X of a school was conducted and the following data was obtained: less than 140: 04, less than 145: 11, less than 150: 29, less than 155: 40, less than 160: 46, less than 165: 51. Find the median height of girls. If mode of the above distribution is 148.05, find the mean using empirical formula.
Board 2025 2 questions
Mode and Mean of a data are 15x and 18x, respectively. Then the median of the data is : (A) x (B) 11x (C) 17x (D) 34x
Find the missing frequency 'f' in the following table, if the mean of the given data is 18. Hence find the mode. Table (Daily Allowance : Number of Children): 11-13 : 7, 13-15 : 6, 15-17 : 9, 17-19 : 13, 19-21 : f, 21-23 : 5, 23-25 : 4.
Sample 2025 4 questions
Consider the frequency distribution of 45 observations. Class: 0-10, 10-20, 20-30, 30-40, 40-50; Frequency: 5, 9, 15, 10, 6. The upper limit of median class is A) 20 B) 10 C) 30 D) 40
Which of the following gives the middle most observation of the data? A) Median B) Mean C) Range D) Mode
Find the mean and median of the following data: Class: 85-90, 90-95, 95-100, 100-105, 105-110, 110-115; frequency: 15, 22, 20, 18, 20, 25.
The monthly expenditure on milk in 200 families of a Housing Society is given below. Monthly Expenditure (in Rs.): 1000-1500, 1500-2000, 2000-2500, 2500-3000, 3000-3500, 3500-4000, 4000-4500, 4500-5000; Number of families: 24, 40, 33, x, 30, 22, 16, 7. Find the value of x and also find the mean expenditure.
Board 2024 5 questions
For some data x1, x2, ...... xn with respective frequencies f1, f2, ..... fn, the value of sum from 1 to n of fi(xi - xbar) is equal to: (a) n*xbar (b) 1 (c) sum of fi (d) 0
The middle most observation of every data arranged in order is called: (a) mode (b) median (c) mean (d) deviation
[case context: BINGO game with 75 numbered balls; grouped frequency table of 48 announced numbers in classes 0-15(8), 15-30(9), 30-45(10), 45-60(12), 60-75(9).] Write the median class.
[case context: BINGO game with 75 numbered balls; grouped frequency table of 48 announced numbers in classes 0-15(8), 15-30(9), 30-45(10), 45-60(12), 60-75(9).] Find median of the given data.
[case context: BINGO game with 75 numbered balls; grouped frequency table of 48 announced numbers in classes 0-15(8), 15-30(9), 30-45(10), 45-60(12), 60-75(9).] Find mode of the given data.
Board 2023 6 questions
The distribution below gives the marks obtained by 80 students on a test: Marks: Less than 10 / 20 / 30 / 40 / 50 / 60; Number of Students: 3 / 12 / 27 / 57 / 75 / 80. The modal class of this distribution is: (A) 10-20 (B) 20-30 (C) 30-40 (D) 50-60
If the value of each observation of a statistical data is increased by 3, then the mean of the data (A) remains unchanged (B) increases by 3 (C) increases by 6 (D) increases by 3n
[case context: IMD table of sub-division wise monsoon rainfall (mm) in 2018 - classes 200-400 to 1600-1800 with frequencies 2,4,7,4,2,3,1,1] Write the modal class.
[case context: IMD table of sub-division wise monsoon rainfall (mm) in 2018 - classes 200-400 to 1600-1800 with frequencies 2,4,7,4,2,3,1,1] If sub-division having at least 1000 mm rainfall during monsoon season, is considered good rainfall sub-division, then how many sub-divisions had good rainfall?
[case context: IMD table of sub-division wise monsoon rainfall (mm) in 2018 - classes 200-400 to 1600-1800 with frequencies 2,4,7,4,2,3,1,1] Find the median of the given data.
[case context: IMD table of sub-division wise monsoon rainfall (mm) in 2018 - classes 200-400 to 1600-1800 with frequencies 2,4,7,4,2,3,1,1] Find the mean rainfall in this season.
Board 2022 3 questions
Find the mode of the following frequency distribution : Class 10-20, 20-30, 30-40, 40-50, 50-60 with frequencies 15, 10, 12, 17, 4 respectively.
For what value of x, is the median of the following frequency distribution 34.5? Class 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70 with frequencies 3, 5, 11, 10, x, 3, 2 respectively.
Following is the daily expenditure on lunch by 30 employees of a company: Daily Expenditure (in Rupees) 100-120, 120-140, 140-160, 160-180, 180-200 with number of employees 8, 3, 8, 6, 5 respectively. Find the mean daily expenditure of the employees.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 13 Statistics?
By how often and how recently they were asked: Empirical relationship / mixed central tendency problems; Median of grouped data; Mean of grouped data (direct / assumed mean / step deviation).
How many marks does Statistics carry in the CBSE Class 10 Mathematics (Standard) exam?
Statistics is part of the Statistics & Probability unit, which carries 11 marks in the official syllabus. In the analysed papers it had about 3.6 questions per paper.
Do questions from Statistics repeat in board exams?
Yes — 8 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.