JEE Main 2020 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 8 January 2020, Shift 1, Maths Q67

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

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q, where

p\neq 0

and

q\neq 0

. If the new mean and new s.d. become half of their original values, then q is equal to :

(1) $-5$
(2) $10$
(3) $-10$
(4) $-20$ Official answer

Official answer

Option 4

NTA final key (Jan 2020).

Chapter: Statistics
Topic: Variance and SD
Idea tested: Effect of Linear Transformations

Same idea in other shifts

Asked 4× in all

18 Mar 2021, Shift 2 · Q64Let in a series of $2n$ observations, half of them are equal to a and remaining half are equal to $-$ a. Also by adding a constant b in…MediumSingle correct
9 Jan 2020, Shift 1 · Q68Let the observations $x_i(1\le i\le 10)$ satisfy the equations, $\sum_{i=1}^{10}(x_i-5)=10$ and $\sum_{i=1}^{10}(x_i-5)^2=40$ . If $\mu$ …MediumSingle correct
2 Sep 2020, Shift 1 · Q67Let $X=\{x\in\mathbf{N} : 1\le x\le 17\}$ and $Y=\{ax+b : x\in X$ and $a, b\in\mathbf{R}, a>0\}$ . If mean and variance of elements of Y…MediumSingle 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.