JEE Main 2023MathematicsStatisticsMediumMCQ

JEE Main 2023 — Statistics Question with Solution

JEE Main 2023 (01 Feb Shift 1)

Question

The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1,3,5, then the sum of cubes of the remaining two observations is

Choose an option

Show full solutionCorrect option: A
Correct answer
A1072

Step-by-step explanation

Let the two observations be a and b.

Given:

Mean=5

⇒1+3+5+a+b5=5

⇒a+b=16        …1

And

σ2=∑xi25-∑xi52

⇒8=12+32+52+a2+b25-25

⇒a2+b2=130      …2

Solving 1 & 2, we get

16-b2+b2=130

⇒b=9

So a=7

Hence, a3+b3=343+729=1072

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About this question

This is a previous-year question from JEE Main 2023, 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.