JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 31 August 2021, Shift 2, Maths Q77

Question 77 of 90 in this shift, Maths question 17 of 30, Section A.

The 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 observations is :

(1) $\frac{92}{5}$
(2) $\frac{536}{25}$ Official answer
(3) $\frac{112}{5}$
(4) $\frac{134}{5}$

Official answer

Option 2

NTA final key.

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.