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Sunday, 25 October

JEE Main · Maths · Class 11

Statistics: JEE Main previous year questions

82 questions in 80 of the 108 JEE Main shifts Lumi analysed, asked in 7 of 8 years. Here is what this chapter tests and how.

Study this chapter
Questions
82
in 80 of 108 shifts · 7 of 8 years
Average a shift
0.6
of 25 Maths · 0.7 since 2024 0.1
Typical range
0.5–1.0
questions a shift; fewest 0.0, most 1.0
Weighted estimate
0.7
model, recent years count more · about 2.9 marks
  • Typical range (fact)
  • Average a shift (fact)
  • Weighted estimate (model)

Questions are counted per shift, out of the 25 each subject has, in the shifts Lumi analysed; papers that offered 30 a subject (2017, 2021–2024) are scaled to 25. Typical range: the middle six of the eight years (2017, 2020–2026), leaving out the single highest and lowest year. The average and the range are historical fact. The weighted estimate is a model: each year's share, with recent years counting more (half-life three years), and chapters NTA dropped from the syllabus set near zero. It is a guide to effort, not a forecast of the paper.

What to do

How to spend time on Statistics

Priority

Lower priority

One of the 7 Maths chapters that shared the last fifth of Maths questions in the 108 shifts analysed. How bands are set

Past questions
82in 80 of 108 shifts
Study plan gives it
14 hover 12 months; 11 h over 6
Study this chapter →

Ideas asked most often

  1. Finding Unknown Observations from Mean and Variance22×
  2. Correcting Incorrect Variance10×
  3. Combined Variance of Two Sets7×
  4. Mean of Discrete Data6×
  5. Effect of Linear Transformations4×

39 of the 62 ideas in Lumi’s map of this chapter have not been asked or touched in the shifts analysed. Of its idea-tagged questions from 2024 on, 21% tested an idea not asked in an earlier year, so learn the whole chapter, not just the list above.

Within each subject, chapters in NTA's 2026 syllabus are ranked by their average questions a shift over all 8 years analysed (history, not the model). Going down that list, the chapters that together held the first half of the subject's questions are Must do; the next ones, up to 80%, are Should do; the rest are Lower priority.

Key findings

Statistics at a glance

  1. 01

    79%

    of its 19 questions from 2024 on that Lumi matched to an idea tested one JEE Main had asked in an earlier year; 100% came from a topic asked in an earlier year.

  2. 02

    63%

    of the 62 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    38%

    of its questions asked for a numerical answer, 1.3 times the Maths average.

  4. 04

    9%

    of its questions were rated hard, against 26% across all Maths questions in the same shifts.

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

0240’170.9’200.6’210.5’221’230.6’240.5’251’26

Raw count: 2017: 0 in 1 shift · 2020: 11 in 12 shifts · 2021: 18 in 24 shifts · 2022: 14 in 24 shifts · 2023: 14 in 12 shifts · 2024: 12 in 18 shifts · 2025: 4 in 8 shifts · 2026: 9 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Numerical answer38%
  • Calculation35%
  • Multi-step24%
  • Conceptual1%
  • Application1%

Most common asks: find unknown data from mean and variance (31); find n from mean and variance (1); mean of terms of product sequence (1).

Profile

This chapter in numbers

Where it ranks, how steady it is, and what it costs to study.

Rank, all JEE chapters
#57
of 70 by weighted estimate
Rank in Maths
#18
of 21 chapters
Share of Maths
2.5%
of its questions, all shifts analysed
Busiest year
2023
1.0 questions a shift
Year to year
Swings a lot
varies by about 0.3 questions a shift
Long-run direction
+0.07
questions a shift, per year
Easy questions
21%
9% rated hard
Numerical answer
38%
1.3× the Maths rate
With a figure
7%
graph, diagram or structure
Study time
14 h
11 h on a 6-month plan
Marks per study hour
0.20
#65 of 70 chapters
Foundation for others
75%
of its ideas are used in other chapters

Difficulty, year by year

Each question rated easy, medium or hard. Each bar is that year’s split, so years compare directly; the number is the questions in that year’s analysed shifts (1 to 24 shifts a year).

  • 2017
  • 202011
  • 202118
  • 202214
  • 202314
  • 202412
  • 20254
  • 20269
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Calculation63%
  • Multi-step34%
  • Application1%
  • Conceptual1%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 62 ideas. In the 108 shifts analysed, JEE Main built a question around 20 of them. Most of the chapter has never been the main idea of a question, so past questions alone leave most of it out.

Asked as the main idea
20
Touched on in a question
3
Never asked
39

Topics

What repeats, topic by topic

This chapter's questions per topic in each year's analysed shifts. The number is the count; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. 11 questions had no close topic in Lumi's map and count for the chapter only.

’17’20’21’22’23’24’25’26
017+questions in that year’s analysed shifts, shaded per shift
  • Variance and SD

    As a topic: 72 questions in 7 of 8 years, most often single correct, 40% numerical answer. Recent asks: combined variance of two sets; mean to SD ratio from shifted square sums; find unknown observations from mean and variance.

  • AP and GP

    As a topic: 136 questions in 8 of 8 years, most often single correct, 32% numerical answer. Recent asks: sum of series then solve for angle; combined AP and GP parameter problem; numerical: GP sum from trig extrema.

Drill down

Topic, idea, question

Open a topic to see every idea JEE Main tested inside it, then open an idea to read the questions. Each row shows its 8 years.

  • Open70 · 85%11171013946

    19 ideas inside

    • OpenRepeated22 · 31%254343
    • OpenRepeated10 · 14%33
    • OpenRepeated7 · 10%42
    • OpenRepeated6 · 9%3
    • OpenRepeated4 · 6%3
    • OpenRepeated3 · 4%2
    • OpenRepeated3 · 4%2
    • OpenRepeated3 · 4%
    • OpenRepeated2 · 3%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
  • Open1 · 1%

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

The exact ideas JEE Main has asked

Inside the topics, 20 different ideas were tested; 11 came more than once. These are the repeats, then the ideas new since 2024.

Dots are the 8 years with analysed shifts, 2017 to 2026.

Every question

All 82 Statistics questions

Newest first, shift by shift. The newest 40 show their opening words; older ones name the idea they tested. Each opens with its options and the official answer.

JEE Main 20269 questions

  1. 2 Apr 2026, Shift 1 · Q8If the mean of the data | Class | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | | Frequency | 2 | kk | 28 | 54 | k+1k+1 | 5 | is 2121,…MediumSingle correct
  2. 2 Apr 2026, Shift 2 · Q9The mean and variance of nn observations are 8 and 16, respectively. If the sum of the first (n−1)(n - 1) observations is 48 and the sum of…EasySingle correct
  3. 4 Apr 2026, Shift 1 · Q10Suppose that the mean and median of the non-negative numbers 21,8,17,a,51,103,b,13,6721, 8, 17, a, 51, 103, b, 13, 67, (a>b)(a>b), are 4040 and 2121, respectively.…HardSingle correct
  4. 4 Apr 2026, Shift 2 · Q8For 10 observations x1,x2,…,x10x_1,x_2,\ldots,x_{10}, if ∑i=110(xi+2)2=180\sum_{i=1}^{10}(x_i+2)^2=180 and ∑i=110(xi−1)2=90\sum_{i=1}^{10}(x_i-1)^2=90, then their standard…MediumSingle correct
  5. 5 Apr 2026, Shift 1 · Q8The mean deviation about the mean for the data | xix_i | 5 | 7 | 9 | 10 | 12 | 15 | | fif_i | 8 | 6 | 2 | 2 | 2 | 6 | is equal to:EasySingle correctHas a figure
  6. 5 Apr 2026, Shift 2 · Q10A variable X takes values 0,0,2,6,12,20,…,n(n−1)0, 0, 2, 6, 12, 20, \dots, n(n-1) with frequencies…HardSingle correct
  7. 6 Apr 2026, Shift 1 · Q9A data consists of 20 observations x1,x2,…,x20x_1, x_2,\ldots, x_{20}. If ∑i=120(xi+5)2=2500\sum_{i=1}^{20}(x_i+5)^2=2500 and ∑i=120(xi−5)2=100\sum_{i=1}^{20}(x_i-5)^2=100, then…MediumSingle correct
  8. 6 Apr 2026, Shift 2 · Q8Let the mean and the variance of seven observations 2,4,α,8,β,12,142, 4, \alpha, 8, \beta, 12, 14, α<β\alpha<\beta, be 8 and 16 respectively. Then the…MediumSingle correct
  9. 8 Apr 2026, Shift 2 · Q7A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of…EasySingle correct

JEE Main 20254 questions

  1. 2 Apr 2025, Shift 2 · Q8If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then a+b+aba+b+ab is equal to :MediumSingle correct
  2. 3 Apr 2025, Shift 2 · Q9Let the Mean and Variance of five observations x1=1,x2=3,x3=a,x4=7x_1 = 1, x_2 = 3, x_3 = a, x_4 = 7 and x5=b, a>bx_5 = b,\ a > b, be 5 and 10 respectively. Then…MediumSingle correct
  3. 4 Apr 2025, Shift 2 · Q8Let the mean and the standard deviation of the observation 2, 3, 3, 4, 5, 7, a, b be 4 and 2\sqrt{2} respectively. Then the mean…MediumSingle correct
  4. 7 Apr 2025, Shift 1 · Q9The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40.…EasySingle correct

JEE Main 202412 questions

  1. 4 Apr 2024, Shift 1 · Q20Let α,β∈R\alpha, \beta \in \mathbf{R}. Let the mean and the variance of 6 observations −3,4,7,−6,α,β-3, 4, 7, -6, \alpha, \beta be 2 and 23,…MediumSingle correct
  2. 6 Apr 2024, Shift 1 · Q18The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation…EasySingle correct
  3. 8 Apr 2024, Shift 2 · Q30Let a,b,c∈Na, b, c \in \mathbb{N} and a<b<ca < b < c. Let the mean, the mean deviation about the mean and the variance of the 5 observations…HardNumerical value
  4. 9 Apr 2024, Shift 1 · Q19The frequency distribution of the age of students in a class of 40 students is given below. | Age | 15 | 16 | 17 | 18 | 19 | 20 |…HardSingle correct
  5. 9 Apr 2024, Shift 2 · Q19If the variance of the frequency distribution | xx | cc | 2c2c | 3c3c | 4c4c | 5c5c | 6c6c | |---|---|---|---|---|---|---| | ff | 2 | 1…MediumSingle correct
  6. 1 Feb 2024, Shift 1 · Q18Let the median and the mean deviation about the median of 7 observation 170, 125, 230, 190, 210, a, b be 170 and 2057\frac{205}{7}…MediumSingle correct
  7. 1 Feb 2024, Shift 2 · Q19Consider 1010 observations x1,x2,…,x10x_1, x_2, \ldots, x_{10} such that ∑i=110(xi−α)=2\sum_{i=1}^{10}(x_i-\alpha)=2 and ∑i=110(xi−β)2=40\sum_{i=1}^{10}(x_i-\beta)^2=40,…MediumSingle correct
  8. 27 Jan 2024, Shift 1 · Q20Let a1,a2,…a10a_1, a_2, \ldots a_{10} be 10 observations such that ∑k=110ak=50\sum_{k=1}^{10}a_k=50 and ∑∀k<jak⋅aj=1100\sum_{\forall k<j}a_k\cdot a_j=1100. Then the…MediumSingle correct
  9. 29 Jan 2024, Shift 1 · Q30If the mean and variance of the data 65,68,58,44,48,45,60,α,β,6065, 68, 58, 44, 48, 45, 60, \alpha, \beta, 60 where α>β\alpha>\beta, are 56 and 66.2 respectively,…MediumNumerical value
  10. 30 Jan 2024, Shift 1 · Q19Let MM denote the median of the following frequency distribution Class: 0−40-4, 4−84-8, 8−128-12, 12−1612-16, 16−2016-20 Frequency: 33, 99, 1010,…MediumSingle correctHas a figure
  11. 30 Jan 2024, Shift 2 · Q30The variance σ2\sigma^2 of the data | xix_i | 0 | 1 | 5 | 6 | 10 | 12 | 17 | |---|---|---|---|---|---|---|---| | fif_i | 3 | 2 | 3 | 2 | 6…EasyNumerical value
  12. 31 Jan 2024, Shift 2 · Q18Let the mean and the variance of 6 observations a,b,68,44,48,60a, b, 68, 44, 48, 60 be 55 and 194, respectively. If a>ba>b, then a+3ba+3b isMediumSingle correct

JEE Main 202314 questions

  1. 6 Apr 2023, Shift 1 · Q17The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and…MediumSingle correct
  2. 6 Apr 2023, Shift 2 · Q29If the mean and variance of the frequency distribution xix_i: 2, 4, 6, 8, 10, 12, 14, 16 fif_i: 4, 4, α\alpha, 15, 8, β\beta, 4, 5 are 9…MediumNumerical valueHas a figure
  3. 8 Apr 2023, Shift 1 · Q30Let the mean and variance of 8 numbers x,y,10,12,6,12,4,8x,y,10,12,6,12,4,8 be 9 and 9.25 respectively. If x>yx>y, then 3x−2y3x-2y is equal to __________.MediumNumerical value
  4. 8 Apr 2023, Shift 2 · Q18Let the mean and variance of 12 observations be 92\frac{9}{2} and 44 respectively. Later on, it was observed that two observations were…MediumSingle correct
  5. 10 Apr 2023, Shift 1 · Q30If the mean of the frequency distribution | Class : | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | | Frequency : | 2 | 3 | xx | 5 | 4 | is 28,…MediumNumerical valueHas a figure
  6. 10 Apr 2023, Shift 2 · Q19Let μ\mu be the mean and σ\sigma be the standard deviation of the distribution xix_i: 00, 11, 22, 33, 44, 55 fif_i: k+2k+2, 2k2k,…MediumSingle correctHas a figure
  7. 11 Apr 2023, Shift 1 · Q13Let x1,x2,…,x100x_1, x_2, \ldots, x_{100} be in an arithmetic progression, with x1=2x_1 = 2 and their mean equal to 200. If…MediumSingle correct
  8. 11 Apr 2023, Shift 1 · Q18Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the…MediumSingle correct
  9. 11 Apr 2023, Shift 2 · Q18Let the mean of 66 observations 1,2,4,5,x1, 2, 4, 5, x and yy be 55 and their variance be 1010. Then their mean deviation about the mean is…MediumSingle correct
  10. 12 Apr 2023, Shift 1 · Q18Two dice A and B are rolled. Let the numbers obtained on A and B be α\alpha and β\beta respectively. If the variance of α−β\alpha-\beta…MediumSingle correct
  11. 12 Apr 2023, Shift 1 · Q24Let the positive numbers a1,a2,a3,a4a_1, a_2, a_3, a_4 and a5a_5 be in a G.P. Let their mean and variance be 3110\frac{31}{10} and mn\frac{m}{n}…HardNumerical value
  12. 13 Apr 2023, Shift 1 · Q29Let the mean of the data | xx | 1 | 3 | 5 | 7 | 9 | | Frequency (ff) | 4 | 24 | 28 | α\alpha | 8 | be 5. If mm and σ2\sigma^2 are…MediumNumerical value
  13. 13 Apr 2023, Shift 2 · Q29The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks…EasyNumerical value
  14. 15 Apr 2023, Shift 1 · Q19The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded…EasySingle correct

JEE Main 202214 questions

  1. 25 Jul 2022, Shift 2 · Q18If the mean deviation about median for the numbers 3,5,7,2k,12,16,21,243,5,7,2k,12,16,21,24, arranged in the ascending order, is 6 then the median isMediumSingle correct
  2. 26 Jul 2022, Shift 2 · Q26Updating Variance After Removing an Observation · Medium · Numerical value
  3. 27 Jul 2022, Shift 1 · Q22Correcting Incorrect Variance · Easy · Numerical value
  4. 28 Jul 2022, Shift 1 · Q28GP Sum of Squares · Medium · Numerical value
  5. 29 Jul 2022, Shift 1 · Q22Relationship Between RMS, Mean, and Variance · Medium · Numerical value
  6. 30 Jul 2022, Shift 2 · Q78Open the question · Medium · Single correct
  7. 25 Jun 2022, Shift 2 · Q25Open the question · Medium · Numerical value
  8. 26 Jun 2022, Shift 1 · Q18Finding Unknown Observations from Mean and Variance · Medium · Single correct
  9. 26 Jun 2022, Shift 2 · Q17Correcting Incorrect Variance · Medium · Single correct
  10. 27 Jun 2022, Shift 2 · Q16Finding Unknown Observations from Mean and Variance · Medium · Single correct
  11. 28 Jun 2022, Shift 1 · Q23Correcting Incorrect Variance · Easy · Numerical value
  12. 28 Jun 2022, Shift 2 · Q22Maximum Variance of Bounded Data · Medium · Numerical value
  13. 29 Jun 2022, Shift 1 · Q20Finding Unknown Observations from Mean and Variance · Medium · Single correct
  14. 29 Jun 2022, Shift 2 · Q17Finding Unknown Observations from Mean and Variance · Medium · Single correct

JEE Main 202118 questions

  1. 3 Aug 2021, Shift 1 · Q77Variance via Arbitrary Point Deviations · Easy · Single correct
  2. 3 Aug 2021, Shift 2 · Q88Finding Unknown Observations from Mean and Variance · Medium · Numerical value
  3. 4 Aug 2021, Shift 2 · Q77Finding Unknown Observations from Mean and Variance · Medium · Single correct
  4. 26 Aug 2021, Shift 1 · Q80Correcting Incorrect Variance · Medium · Single correct
  5. 26 Aug 2021, Shift 2 · Q86Finding Unknown Observations from Mean and Variance · Medium · Numerical value
  6. 27 Aug 2021, Shift 1 · Q88Variance of First n Naturals · Easy · Numerical value
  7. 27 Aug 2021, Shift 2 · Q90Combined Variance of Two Sets · Medium · Numerical value
  8. 31 Aug 2021, Shift 1 · Q90Mean of Discrete Data · Medium · Numerical value
  9. 31 Aug 2021, Shift 2 · Q77Finding Unknown Observations from Mean and Variance · Medium · Single correct
  10. 24 Feb 2021, Shift 2 · Q81Finding Unknown Observations from Mean and Variance · Medium · Numerical value
  11. 26 Feb 2021, Shift 2 · Q85Minimum Sum of Squared Deviations · Medium · Numerical value
  12. 22 Jul 2021, Shift 2 · Q89Mean of Discrete Data · Medium · Numerical value
  13. 25 Jul 2021, Shift 1 · Q86Open the question · Medium · Numerical value · has a figure
  14. 25 Jul 2021, Shift 2 · Q68Combined Variance of Two Sets · Medium · Single correct
  15. 16 Mar 2021, Shift 2 · Q86Combined Variance of Two Sets · Easy · Numerical value
  16. 17 Mar 2021, Shift 2 · Q84Combined Variance of Two Sets · Hard · Numerical value
  17. 18 Mar 2021, Shift 1 · Q87Mean of Discrete Data · Easy · Numerical value
  18. 18 Mar 2021, Shift 2 · Q64Effect of Linear Transformations · Medium · Single correct

JEE Main 202011 questions

  1. 8 Jan 2020, Shift 1 · Q67Effect of Linear Transformations · Medium · Single correct
  2. 8 Jan 2020, Shift 2 · Q68Correcting Incorrect Variance · Easy · Single correct
  3. 9 Jan 2020, Shift 1 · Q68Effect of Linear Transformations · Medium · Single correct
  4. 2 Sep 2020, Shift 1 · Q67Effect of Linear Transformations · Medium · Single correct
  5. 2 Sep 2020, Shift 2 · Q75Variance of an Arithmetic Progression · Medium · Numerical value
  6. 3 Sep 2020, Shift 1 · Q67Maximum Variance of Bounded Data · Hard · Single correct
  7. 3 Sep 2020, Shift 2 · Q67Variance via Arbitrary Point Deviations · Easy · Single correct
  8. 4 Sep 2020, Shift 1 · Q68Finding Unknown Observations from Mean and Variance · Medium · Single correct
  9. 4 Sep 2020, Shift 2 · Q71Finding Unknown Frequency via Variance · Easy · Numerical value
  10. 5 Sep 2020, Shift 1 · Q68Finding Unknown Observations from Mean and Variance · Medium · Single correct
  11. 6 Sep 2020, Shift 2 · Q75Mean of Discrete Data · Medium · Numerical value

Questions from the official JEE Main papers published by NTA. Chapter, topic and idea tags, counts and notes are Lumi’s. Pattern: Asked most years.

More Maths, Class 11

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