JEE Main 2020 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 3 September 2020, Shift 2, Maths Q67

Question 67 of 75 in this shift, Maths question 17 of 25.

Let

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

\sum_{i=1}^{10}(x_i - p)^2 = 9

where

0 \neq p \in \mathbf{R}

, then the standard deviation of these observations is :

(1) $\frac{9}{10}$ Official answer
(2) $\frac{7}{10}$
(3) $\frac{4}{5}$
(4) $\sqrt{\frac{3}{5}}$

Official answer

Option 1

NTA final key (Sep 2020).

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 Aug 2021, Shift 1 · Q77If $\sum_{i=1}^{16} a_i - 6 = 8$ and $\sum_{i=1}^{16} a_i - 6^{\,2} = 40$ , then the standard deviation of $a_1, a_2, \ldots, a_{16}$ isEasySingle 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.