JEE Main 2023MathematicsStatisticsEasyMCQ

JEE Main 2023 — Statistics Question with Solution

JEE Main 2023 (25 Jan Shift 1)

Question

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12 . If the new mean of the marks is 10.2. then their new variance is equal to:

Choose an option

Show full solutionCorrect option: C
Correct answer
C3.96

Step-by-step explanation

Let the number of observations of the data set is n.

So,

∑xi=10n   ....i

Also,

∑xi-8+12=10.2n

⇒10n+4=10.2n

⇒0.2n=4

⇒n=20

Also,

σ2=4=∑xi220-100

⇒∑xi2=104×20=2080

Now, new variance is

=∑xi2-82+12220-10.22

=2080+4×2020-104.04

=108-104.04

=3.96

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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.