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Saturday, 31 October

JEE Main · Maths · Statistics

Variance via Arbitrary Point Deviations

JEE Main asked Variance via Arbitrary Point Deviations 3 times in 3 of the 108 shifts Lumi analysed, in 2020, 2021 and 2024. It belongs to Variance and SD, in Statistics (Maths). The longest wait between two years asking it was 3 years.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2020
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170.08’200.03’210’220’230.05’240’250’26

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

Shift by shift

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

  • 20260 of 9
  • 20250 of 8
  • 20241 of 18
  • 20230 of 12
  • 20220 of 24
  • 20211 of 24
  • 20201 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: calculation.

  • Find unknown data from mean and variance
  • Standard deviation from deviation sums

Difficulty

Easy 2Medium 1Hard 0

Every question was multiple choice.

Every question

All 3 questions

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

  1. 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
  2. 3 Aug 2021, Shift 1 · Q77If ∑i=116ai−6=8\sum_{i=1}^{16} a_i - 6 = 8 and ∑i=116ai−6 2=40\sum_{i=1}^{16} a_i - 6^{\,2} = 40, then the standard deviation of a1,a2,…,a16a_1, a_2, \ldots, a_{16} isEasySingle correct
  3. 3 Sep 2020, Shift 2 · Q67Let xix_i (1≤i≤10)(1 \leq i \leq 10) be ten observations of a random variable X. If ∑i=110(xi−p)=3\sum_{i=1}^{10}(x_i - p) = 3 and…EasySingle correct

Shifts: 3 Sep 2020, Shift 2, 3 Aug 2021, Shift 1, 1 Feb 2024, 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