JEE Main 2020MathematicsStatisticsMediumMCQ

JEE Main 2020 — Statistics Question with Solution

JEE Main 2020 (04 Sep Shift 1)

Question

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5,7,10,12,14,15, then the absolute difference of the remaining two observations is :

Choose an option

Show full solutionCorrect option: D
Correct answer
D7

Step-by-step explanation

Let remaining two observations are a and b

Σxin=5+7+12+10+15+14+a+b8=10

⇒ 63+a+b=80

⇒ a+b=17

σ2=Σxi2n−Σxin2

⇒13.5=25+49+144+100+225+196+a2+b28−100

⇒908=a2+b2+739

⇒a2+b2=169

⇒a+b2−2ab=169

⇒289−169=2ab

⇒ ab=60

∴ a−b2=a+b2−4ab=289−240=49

∴ a−b=7.

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About this question

This is a previous-year question from JEE Main 2020, 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.