JEE Main 2022MathematicsStatisticsMediumNumerical

JEE Main 2022 — Statistics Question with Solution

JEE Main 2022 (28 Jun Shift 1)

Question

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _____.

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Show full solutionCorrect answer: 17
Correct answer
17

Step-by-step explanation

Old mean=x1+x2+...x14+515=8 (given)

⇒x1+x2+...x14=115

Correct mean=x1+x2+...x14+2015=x¯new⇒x¯new=9

Given, old variance=9⇒x12+x22+...x142+5215-82=9⇒x12+x22+...x142=1070

Now varnew=x12+x22+...x142+20215-92=1070+40015-81=17

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About this question

This is a previous-year question from JEE Main 2022, 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.