JEE Main 2024MathematicsStatisticsEasyNumerical

JEE Main 2024 — Statistics Question with Solution

JEE Main 2024 (29 Jan Shift 1)

Question

If the mean and variance of the data 65,68,58,44, 48,45,60,α,β,60 where α>β are 56 and 66.2 respectively, then α2+β2 is equal to

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Show full solutionCorrect answer: 6344
Correct answer
6344

Step-by-step explanation

Given: x¯=56 and σ2=66.2

We know that, σ2=∑xi2n-x2

⇒652+682+582+442+482+452+602+α2+β2+60210-562=66.2

⇒α2+β2+2567810-(56)2=66.2

⇒α2+β2+2567810=3136+66.2

⇒α2+β2=32022-25678

⇒α2+β2=6344

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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.