JEE Main 2020MathematicsStatisticsMediumMCQ

JEE Main 2020 — Statistics Question with Solution

JEE Main 2020 (08 Jan Shift 1)

Question

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≠0 and q≠0. If the new mean and new s.d. become half of their original values, then q is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C-20

Step-by-step explanation

If each observation is multiplied with p & then q is subtracted, then
New mean x-1=px--q
⇒ 10=p20-q .....1
and new standard deviation
σ2=pσ1 ⇒ 1=p2   ⇒  p=12  ⇒ p=±12
If p=12
then q = 0  (from equation (1))
If p=-12
q=-20

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About this question

This is a previous-year question from JEE Main 2020, covering the Statistics chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.