JEE (Main) · Mathematics, Class 11
Statistics: JEE Main PYQ, 2020–2025
Statistics (Mathematics, Class 11) has been asked 78 times in the 111 JEE (Main) shift papers from 2020–2025: about 0.7 questions a paper, 3% of all Mathematics questions. It is the 19th most-asked of 19 Mathematics chapters. The 2025 shifts had 7 from it in all. Last checked 28 October 2026.
Questions per year, all shifts
Year by year.
| Year | Questions |
|---|---|
| 2020 | 13in 14 papers |
| 2021 | 20in 26 papers |
| 2022 | 14in 24 papers |
| 2023 | 12in 12 papers |
| 2024 | 12in 18 papers |
| 2025 | 7in 17 papers |
JEE (Main) is sat in many shifts a year, each with its own paper; the counts add up every shift. 2021–2024 papers had 30 questions a subject, the others 25.
Inside the chapter
Topics asked most.
- Standard deviation and variance60
- Mean deviation9
- Mean, median and mode9
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10 Statistics questions to practise.
Our own questions, written in the JEE Main pattern and checked, each with an explanation. Pick an option to see the answer.
Q1 · Mathematics · Statistics
The mean deviation about the mean of 40 observations x₁, …, x₄₀ is 2.5. Each observation is replaced by yᵢ = 4xᵢ − 7. What is the mean deviation of the y-values about their mean?
Answer: (A)
The new mean is ȳ = 4x̄ − 7, so yᵢ − ȳ = 4(xᵢ − x̄) and |yᵢ − ȳ| = 4|xᵢ − x̄|. Averaging gives a mean deviation of 4 × 2.5 = 10.
Q2 · Mathematics · Statistics
In a set of 100 observations, 25 are equal to 4 and the remaining 75 are equal to 12. The variance of the 100 observations is
Answer: (A)
Mean = (25 × 4 + 75 × 12)/100 = 10. Σfx²/N = (25 × 16 + 75 × 144)/100 = 112. Variance = 112 − 10² = 12. As a check, the deviations are −6 and +2, so the variance is (25 × 36 + 75 × 4)/100 = 12.
Q3 · Mathematics · Statistics
How many different sets of five positive integers (repetitions allowed, order irrelevant) have mean 12, median 15 and a unique mode equal to 18?
Answer: (A)
Write the data in ascending order as a ≤ b ≤ c ≤ d ≤ e. The median is c = 15. The sum is 5 × 12 = 60. A unique mode of 18 means 18 appears at least twice and more often than any other value. Since 18 > 15, the 18s must sit at d and e, so d = e = 18. Then a + b = 60 − 15 − 36 = 9. If a = b, 18 would not be the unique mode, but 9 is odd so a ≠ b anyway. With positive integers and a < b the pairs are (1, 8), (2, 7), (3, 6), (4, 5), all with b ≤ 15. Hence 4 sets.
Q4 · Mathematics · Statistics
What is the arithmetic mean of the first 25 natural numbers?
Answer: (B)
The sum of the first n natural numbers is n(n+1)/2, so their mean is (n+1)/2. For n = 25 the mean is 26/2 = 13. Choosing 12.5 uses n/2. Choosing 14 uses a wrong formula. Choosing 325 stops at the sum and forgets to divide.
Q5 · Mathematics · Statistics
Six observations have a mean deviation about their mean equal to 8. A seventh observation, equal to the mean of the first six, is added. What is the mean deviation of all seven observations about their mean?
Answer: (D)
The original sum of absolute deviations is 6 x 8 = 48. The new observation equals the mean, so the mean stays the same and the new observation contributes a deviation of 0. The sum is still 48, but there are now 7 observations. The new MD = 48/7.
Q6 · Mathematics · Statistics
For ten observations x₁, x₂, …, x₁₀ it is given that Σ(xᵢ − 3)² = 100 and Σ(xᵢ − 5)² = 60. What is the variance of the observations?
Answer: (A)
For any real a, Σ(xᵢ − a)² = Σ(xᵢ − x̄)² + n(x̄ − a)² = nσ² + n(x̄ − a)². Then 100 = 10σ² + 10(x̄ − 3)² and 60 = 10σ² + 10(x̄ − 5)². Subtracting gives 40 = 10[(x̄ − 3)² − (x̄ − 5)²] = 10(4x̄ − 16), so x̄ = 5. Substituting back, 60 = 10σ² + 0, so σ² = 6. Check: 10σ² + 10(5 − 3)² = 60 + 40 = 100.
Q7 · Mathematics · Statistics
Series A has mean 50 and standard deviation 5. Series B has mean 20 and standard deviation 3. Which statement correctly compares the consistency (relative variability) of the two series?
Answer: (A)
To compare variability when the means differ, use the coefficient of variation CV = (σ/x̄) × 100. For A, CV = 5/50 × 100 = 10%. For B, CV = 3/20 × 100 = 15%. The series with the smaller CV is more consistent, so A is.
Q8 · Mathematics · Statistics
Group A has 30 observations with mean 40 and standard deviation 3. Group B has 20 observations with mean 50 and standard deviation 7. What is the standard deviation of the combined 50 observations?
Answer: (A)
The combined mean is (30·40 + 20·50)/50 = 44. The deviations of the group means from it are d₁ = −4 and d₂ = 6. The combined variance is [n₁(σ₁² + d₁²) + n₂(σ₂² + d₂²)]/(n₁ + n₂) = [30(9 + 16) + 20(49 + 36)]/50 = (750 + 1700)/50 = 49. The standard deviation is 7. The combined spread includes the variation between the group means as well as the variation within each group.
Q9 · Mathematics · Statistics
A frequency distribution has class intervals 0–10, 10–20, 20–30, 30–40, 40–50 with frequencies 4, 8, x, 12, 6 respectively. Its mean is 27. What is its variance?
Answer: (D)
The class marks are 5, 15, 25, 35, 45. Σfx = 20 + 120 + 25x + 420 + 270 = 830 + 25x, and the mean condition gives 830 + 25x = 27(30 + x), so x = 10 and N = 40. The deviations about 27 are −22, −12, −2, 8, 18, so Σf(x − 27)² = 4(484) + 8(144) + 10(4) + 12(64) + 6(324) = 1936 + 1152 + 40 + 768 + 1944 = 5840. The variance is 5840/40 = 146.
Q10 · Mathematics · Statistics
The observations 14, 27, 9, 31, 22, 18 are given. What is the range of this data?
Answer: (A)
The range is the simplest measure of dispersion: Range = maximum value − minimum value. Scan the data: the maximum is 31 and the minimum is 9. Therefore Range = 31 − 9 = 22.
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All 78 real JEE Main questions from Statistics.
The questions from the actual papers, with the official answer and an explanation for each — chapter by chapter, or as full timed papers.
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About Statistics in JEE Main.
How many questions come from Statistics in JEE Main?
Statistics (Mathematics, Class 11) has been asked 78 times in the 111 JEE (Main) shift papers from 2020–2025: about 0.7 questions a paper, 3% of all Mathematics questions. It is the 19th most-asked of 19 Mathematics chapters. The 2025 shifts had 7 from it in all.
Which topics of Statistics are asked most in JEE Main?
Standard deviation and variance (60), Mean deviation (9), Mean, median and mode (9), counted over the papers from 2020–2025.
Is Statistics important for JEE Main 2027?
It is in the syllabus in force, so it can be asked. By past papers it ranks 19 of 19 in Mathematics; use that to decide how much time it gets, not whether to study it.
Where can I solve Statistics JEE Main previous year questions?
On Nikaalle, free: sign up and practise every past JEE Main question from Statistics with an explanation for each, or sit the full papers timed. The ten questions on this page are our own, written in the same pattern.
Your JEE Main 2027 plan, chapter by chapter.
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