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Friday, 9 October

JEE Main Maths · Class 11

Statistics: JEE Main previous year questions

Statistics had 32 questions in the 42 JEE Main shifts Lumi analysed, about 0.6 a shift, asked in 31 of 42 shifts. It ranks 18 of 22 Maths chapters by questions; 9% of its questions were hard.

Questions
32
in 31 of 42 shifts
A shift, on average
0.6
of 25 Maths questions
Since 2024
+0.1
0.6 a shift in 2017–23, 0.7 in 2024–26
Numerical answer
9
28% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
05100’173’204’212’225’235’244’259’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 2017
  • 20203
  • 20214
  • 20222
  • 20235
  • 20245
  • 20254
  • 20269
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

2 topics and 10 distinct ideas; 6 ideas were asked more than once. Most questions are single correct and calculation.

Topics, by questions

5 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
6 repeat

Study it on Lumi

Statistics: the interactive lesson

Every question

All 32 Statistics questions

Newest first. Each opens with its options and the official answer.

2026 9 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

2025 4 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

2024 5 questions

  1. 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
  2. 9 Apr 2024, Shift 2 · Q19If the variance of the frequency distribution | xx | cc | 2c2c | 3c3c | 4c4c | 5c5c | 6c6c | |---|---|---|---|---|---|---| | ff | 2 | 1…MediumSingle correct
  3. 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
  4. 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
  5. 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

2023 5 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. 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
  3. 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
  4. 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
  5. 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

2022 2 questions

  1. 28 Jul 2022, Shift 1 · Q28Let x1,x2,x3,…,x20x_1,x_2,x_3,\ldots,x_{20} be in geometric progression with x1=3x_1=3 and the common ratio 12\frac{1}{2}. A new data is constructed…MediumNumerical value
  2. 29 Jun 2022, Shift 1 · Q20Let the mean and the variance of 5 observations x1,x2,x3,x4,x5x_1, x_2, x_3, x_4, x_5 be 245\frac{24}{5} and 19425\frac{194}{25} respectively. If the mean…MediumSingle correct

2021 4 questions

  1. 3 Aug 2021, Shift 2 · Q88The mean and variance of 7 observations are 7 and 18 respectively. If 5 of the observations are 2, 4, 10, 11, 13 and the remaining…MediumNumerical value
  2. 25 Jul 2021, Shift 1 · Q86Consider the following frequency distribution : Class : 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 Frequency : α\alpha | 110 | 54 |…MediumNumerical valueHas a figure
  3. 16 Mar 2021, Shift 2 · Q86Consider the statistics of two sets of observations as follows : Size Mean Variance Observation I 10 2 2 Observation II n 3 1 If the…EasyNumerical value
  4. 18 Mar 2021, Shift 1 · Q87The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place.…EasyNumerical value

2020 3 questions

  1. 8 Jan 2020, Shift 1 · Q67The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p…MediumSingle correct
  2. 2 Sep 2020, Shift 1 · Q67Let X={x∈N:1≤x≤17}X=\{x\in\mathbf{N} : 1\le x\le 17\} and Y={ax+b:x∈XY=\{ax+b : x\in X and a,b∈R,a>0}a, b\in\mathbf{R}, a>0\}. If mean and variance of elements of Y…MediumSingle correct
  3. 6 Sep 2020, Shift 2 · Q75Consider the data on xx taking the values 0,2,4,8,…,2n0, 2, 4, 8, \ldots, 2^n with frequencies nC0,nC1,nC2,…,nCn{}^nC_0, {}^nC_1, {}^nC_2, \ldots, {}^nC_n…MediumNumerical value

Pattern: Asked most years.