JEE Main 2021MathematicsStatisticsEasyMCQ

JEE Main 2021 — Statistics Question with Solution

JEE Main 2021 (16 Mar Shift 1)

Question

Consider three observations a,b and c such that b=a+c. If the standard deviation of a+2,c+2 is d, then which of the following is true?

Choose an option

Show full solutionCorrect option: D
Correct answer
Db2=3a2+c2-9d2

Step-by-step explanation

For a,b,c

mean =a+b+c3=x¯

b=a+c

⇒x¯=2b3   ...(1)

S.D.a+2,b+2,c+2=S.D.a,b,c=d

⇒d2=a2+b2+c23-x¯2

⇒d2=a2+b2+c23-4b29

⇒9d2=3a2+b2+c2-4b2

⇒b2=3a2+c2-9d2

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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.