JEE Main 2021MathematicsStatisticsMediumMCQ

JEE Main 2021 — Statistics Question with Solution

JEE Main 2021 (27 Jul Shift 1)

Question

If the mean and variance of the following data: 6,10,7,13,a,12,b,12 are 9 and 374 respectively, then a-b2 is equal to:

Choose an option

Show full solutionCorrect option: D
Correct answer
D16

Step-by-step explanation

Mean =6+10+7+13+a+12+b+128=9

⇒60+a+b=72

⇒a+b=12    ...1

variance =∑xi2n-∑xin2=374

Here, Σxi2=62+102+72+132+a2+b2+122+122

=a2+b2+642

So, variance is a2+b2+6428-92=374

⇒a2+b28+3214-81=374

⇒a2+b28=81+374-3214

⇒a2+b28=81-71

∴ a2+b2=80

From 1 a2+b2+2ab=144

⇒80+2ab=144  ∴ 2ab=64

So, a-b2=a2+b2-2ab=80-64=16.

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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.