JEE Main 2024MathematicsStatisticsMediumMCQ

JEE Main 2024 — Statistics Question with Solution

JEE Main 2024 (29 Jan Shift 2)

Question

If the mean and variance of five observations are 245 and 19425 respectively and the mean of first four observations is 72, then the variance of the first four observations in equal to

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Show full solutionCorrect option: C
Correct answer
C54

Step-by-step explanation

Given: 

x=245 and variance is 19425

⇒∑i=15xi=245×5

⇒∑i=15xi=24

Also, variance

⇒∑i=15xi25-2452=19425

⇒∑i=15xi2=154

Now, 5th observation =24-sum of first 4 terms

=24-72×4=10

So, new variance =∑i=14xi24-722

=154-1004-494

=54

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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.