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Saturday, 31 October

JEE Main · Maths · Statistics

Finding Unknown Observations from Mean and Variance

JEE Main asked Finding Unknown Observations from Mean and Variance 22 times in 22 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Variance and SD, in Statistics (Maths). The longest wait between two years asking it was 1 year. In 2020, 2021, 2022, 2023, 2024 and 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
22
in 22 shifts
Years
7 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.20.40’170.17’200.17’210.14’220.21’230.19’240.38’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 5 in 24 shifts · 2022: 4 in 24 shifts · 2023: 3 in 12 shifts · 2024: 4 in 18 shifts · 2025: 3 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20253 of 8
  • 20244 of 18
  • 20233 of 12
  • 20224 of 24
  • 20215 of 24
  • 20202 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Find unknown data from mean and variance
  • Find unknown observations from mean and variance

Difficulty

Easy 0Medium 20Hard 2

7 of the 22 questions had a numerical answer.

Every question

All 22 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 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
  2. 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
  3. 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
  4. 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
  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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 29 Jun 2022, Shift 2 · Q17The number of values of a∈Na \in \mathbb{N} such that the variance of 3,7,12,a,43−a3, 7, 12, a, 43 - a is a natural number is:MediumSingle correct
  13. 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
  14. 27 Jun 2022, Shift 2 · Q16The mean and variance of the data 4,5,6,6,7,8,x,y4, 5, 6, 6, 7, 8, x, y, where x<yx<y, are 66 and 94\frac{9}{4} respectively. Then x4+y2x^4+y^2 is equal toMediumSingle correct
  15. 26 Jun 2022, Shift 1 · Q18The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M…MediumSingle correct
  16. 24 Feb 2021, Shift 2 · Q81If the variance of 10 natural numbers 1, 1, 1, ..., 1, kk is less than 10, then the maximum possible value of kk is __________.MediumNumerical value
  17. 31 Aug 2021, Shift 2 · Q77The mean and variance of 7 observations are 8 and 16 respetively. If two observations are 6 and 8, then the variance of the remaining 5…MediumSingle correct
  18. 26 Aug 2021, Shift 2 · Q86Let the mean and variance of four numbers 3, 7, xx and yy (x>yx>y) be 5 and 10 respectively. Then the mean of four numbers 3+2x3+2x,…MediumNumerical value
  19. 4 Aug 2021, Shift 2 · Q77The mean and the variance of seven observations are 8 and 16 respectively. If five of the observations are 2, 4, 10, 12 and 14, then the…MediumSingle correct
  20. 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
  21. 5 Sep 2020, Shift 1 · Q68The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute…MediumSingle correct
  22. 4 Sep 2020, Shift 1 · Q68The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the…MediumSingle correct

Shifts: 4 Sep 2020, Shift 1, 5 Sep 2020, Shift 1, 24 Feb 2021, Shift 2, 3 Aug 2021, Shift 2, 4 Aug 2021, Shift 2, 26 Aug 2021, Shift 2, 31 Aug 2021, Shift 2, 26 Jun 2022, Shift 1, 27 Jun 2022, Shift 2, 29 Jun 2022, Shift 2, 29 Jun 2022, Shift 1, 8 Apr 2023, Shift 1, 11 Apr 2023, Shift 2, 12 Apr 2023, Shift 1, 29 Jan 2024, Shift 1, 31 Jan 2024, Shift 2, 4 Apr 2024, Shift 1, 8 Apr 2024, Shift 2, 2 Apr 2025, Shift 2, 3 Apr 2025, Shift 2, 4 Apr 2025, Shift 2, 6 Apr 2026, Shift 2.

Same topic

Other ideas in Variance and SD

Variance and SD has 20 ideas JEE Main has asked; 10 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas