JEE Main 2012 — Statistics Question with Solution
From: AIEEE 2012
Question
Let x1, x2,........., xn be n observations, and let be their arithematic mean and be their variance.
Statement 1 : Variance of 2x1, 2x2,......., 2xn is 4.
Statement 2 : : Arithmetic mean of 2x1, 2x2,......, 2xn is 4.
Statement 1 : Variance of 2x1, 2x2,......., 2xn is 4.
Statement 2 : : Arithmetic mean of 2x1, 2x2,......, 2xn is 4.
Choose an option
Show full solutionCorrect option: D
Correct answer
DStatement 1 is true, statement 2 is false
Step-by-step explanation
Given that,
for
and variance
Now A.M of
But given
Statement is false.
Variance of
Variance of
Variance of
So, statement is correct.
for
and variance
Now A.M of
But given
Statement is false.
Variance of
Variance of
Variance of
So, statement is correct.
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This is a previous-year question from JEE Main 2012, 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.