JEE Main 2021MathematicsStatisticsEasyNumerical

JEE Main 2021 — Statistics Question with Solution

JEE Main 2021 (27 Aug Shift 1)

Question

Let n be an odd natural number such that the variance of 1,2,3,4,…,n is 14. Then n is equal to ________.

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Show full solutionCorrect answer: 13
Correct answer
13

Step-by-step explanation

Variance of n natural number is given by,

Variance=∑n2n-∑nn2=nn+12n+16n-nn+12n2

                  =n+12n+16-n+14=n+1n-112=n2-112

And it is given that Variance=14

⇒n2-112=14

⇒n2-1=168

⇒n=13

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About this question

This is a previous-year question from JEE Main 2021, 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.