JEE Main 2019MathematicsStatisticsMediumMCQ

JEE Main 2019 — Statistics Question with Solution

JEE Main 2019 (09 Jan Shift 2)

Question

A data consists of n observations: x1, x2, … , xn. If ∑i=1nxi+12=9n and ∑i=1nxi-12=5n, then the standard deviation of this data is

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Show full solutionCorrect option: C
Correct answer
C5

Step-by-step explanation

Given:

∑i=1nxi+12=9n

⇒∑i=1nxi2+2xi+1=9n  ...1

And, ∑i=1nxi-12=5n

⇒∑i=1nxi2-2xi+1=5n  ...2 

Form 1+2, we get

∑i=1n2xi2+2=14n 

⇒∑i=1nxi2=6n  ...3 

From 1-2, we get 

⇒∑i=1nxi=n  ...4

∴ Variance, σ2=Ex2-Ex2

⇒σ2=∑x2n-∑xn 

⇒σ2=6nn-nn2=6-1=5

∴ Standard deviation, σ=5.

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About this question

This is a previous-year question from JEE Main 2019, 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.