JEE Main 2021MathematicsStatisticsMediumNumerical

JEE Main 2021 — Statistics Question with Solution

JEE Main 2021 (27 Aug Shift 2)

Question

An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If μ is the average marks of girls and σ2 is the variance of marks of 50 candidates, then μ+σ2 is equal to

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Show full solutionCorrect answer: 25
Correct answer
25

Step-by-step explanation

20 Boys, 30 Girls
σB2=2,X¯B=12σG2=2

X¯G=50×15−20×1230=51030=17=μ
Variance of 50 condidates
σ2=20σB2+30σG220+30+20⋅30(20+30)2X¯B−X¯G2

=20×2+30×250+6002500(25)=8

μ+σ2=17+8=25

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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.