JEE Main 2021MathematicsStatisticsMediumMCQ

JEE Main 2021 — Statistics Question with Solution

JEE Main 2021 (26 Aug Shift 1)

Question

The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. If α and β are the mean and standard deviation respectively for correct data, then (α,β) is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A(10.5,26)

Step-by-step explanation

Mean =x1+x2+x3+……+x19+2520=10⇒x1+x2+x3+………+x19+25=200

⇒x1+x2+x3+………+x19=175

New mean =x1+x2+x3+……+x19+3520=175+3520=10.5

S.D. =x12+x22+x32+……+x192+(25)220-(10)2

⇒2.5=x12+x22+x32+……+x192+(25)220-(10)2

⇒x12+x22+x32+……+x192=1500

New  S.D. =x12+x22+x32+……+x192+(35)220-(10.5)2

=1500+(35)220-(110.25)

=26

(α,β)=(10.5,26)

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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.