JEE Main 2021 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 3 August 2021, Shift 1, Maths Q77

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

\sum_{i=1}^{16} a_i - 6 = 8

and

\sum_{i=1}^{16} a_i - 6^{\,2} = 40

, then the standard deviation of

a_1, a_2, \ldots, a_{16}

(1) $\frac{2}{3}$
(2) $\frac{3}{2}$ Official answer
(3) $\frac{5}{2}$
(4) $\frac{2}{5}$

Official answer

Option 2

NTA final key.

Chapter: Statistics
Topic: Variance and SD
Idea tested: Variance via Arbitrary Point Deviations

Same idea in other shifts

Asked 3× in all

1 Feb 2024, Shift 2 · Q19Consider $10$ observations $x_1, x_2, \ldots, x_{10}$ such that $\sum_{i=1}^{10}(x_i-\alpha)=2$ and $\sum_{i=1}^{10}(x_i-\beta)^2=40$ ,…MediumSingle correct
3 Sep 2020, Shift 2 · Q67Let $x_i$ $(1 \leq i \leq 10)$ be ten observations of a random variable X. If $\sum_{i=1}^{10}(x_i - p) = 3$ and…EasySingle 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.