JEE Main 2024MathematicsStatisticsMediumMCQ

JEE Main 2024 — Statistics Question with Solution

JEE Main 2024 (01 Feb Shift 2)

Question

Consider 10 observation x1,x2,...x10, such that ∑i=110xi−α=2 and ∑i=110xi−β2=40, where α,β are positive integers. Let the mean and the variance of the observations be 65 and 8425 respectively. The βα is equal to:

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Show full solutionCorrect option: A
Correct answer
A2

Step-by-step explanation

Given observations are x1,x2,...,x10

⇒∑i=110xi−α=2

⇒∑i=110xi−10α=2

Mean, μ=65=∑xi10

⇒∑xi=12

⇒10α+2=12

⇒α=1

Now, ∑i=110xi−β2=40. Let yi=xi−β

⇒σy2=110∑yi2−y¯2

⇒8425=110∑xi−β2−∑i=110xi−β102

⇒8425=4−12−10β102

⇒6−5β52=4−8425

⇒6−5β52=1625

⇒6−5β=±4

⇒β=25 (not possible) or β=2

Hence, βα=2

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About this question

This is a previous-year question from JEE Main 2024, 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.