JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 September 2020, Shift 1, Maths Q68

Question 68 of 75 in this shift, Maths question 18 of 25.

The 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 absolute difference of the remaining two observations is :

(1)3
(2)5
(3)7Official answer
(4)9

Official answer

Option 3

NTA final key (Sep 2020).

Chapter: Statistics
Topic: Variance and SD
Idea tested: Finding Unknown Observations from Mean and Variance

Same idea in other shifts

Asked 22× in all

6 Apr 2026, Shift 2 · Q8Let the mean and the variance of seven observations $2, 4, \alpha, 8, \beta, 12, 14$ , $\alpha<\beta$ , be 8 and 16 respectively. Then the…MediumSingle correct
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 $a+b+ab$ is equal to :MediumSingle correct
3 Apr 2025, Shift 2 · Q9Let the Mean and Variance of five observations $x_1 = 1, x_2 = 3, x_3 = a, x_4 = 7$ and $x_5 = b,\ a > b$ , be 5 and 10 respectively. Then…MediumSingle correct
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 $\sqrt{2}$ respectively. Then the mean…MediumSingle correct
4 Apr 2024, Shift 1 · Q20Let $\alpha, \beta \in \mathbf{R}$ . Let the mean and the variance of 6 observations $-3, 4, 7, -6, \alpha, \beta$ be 2 and 23,…MediumSingle correct
8 Apr 2024, Shift 2 · Q30Let $a, b, c \in \mathbb{N}$ and $a < b < c$ . Let the mean, the mean deviation about the mean and the variance of the 5 observations…HardNumerical value
29 Jan 2024, Shift 1 · Q30If the mean and variance of the data $65, 68, 58, 44, 48, 45, 60, \alpha, \beta, 60$ where $\alpha>\beta$ , are 56 and 66.2 respectively,…MediumNumerical value
31 Jan 2024, Shift 2 · Q18Let the mean and the variance of 6 observations $a, b, 68, 44, 48, 60$ be 55 and 194, respectively. If $a>b$ , then $a+3b$ isMediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.