JEE Main 2014MathematicsStatisticsEasyMCQ

JEE Main 2014 — Statistics Question with Solution

JEE Main 2014 (19 Apr Online)

Question

Let x¯, M and σ2 be respectively the mean, mode and variance of n observations x1, x2,...., xn and di=-xi-a, i=1, 2,...., n, where a is any number.

Statement I: Variance of d1, d2,..., dn is σ 2 .

Statement II: Mean and mode of d1, d2,...., dn are -x¯-a and -M-a, respectively.

Choose an option

Show full solutionCorrect option: A
Correct answer
AStatement I and Statement II are both true 

Step-by-step explanation

Mean of d1, d2, d3... dn

=∑i=1n  -xi-a n 

=-∑i=1n xi n+ -a n∑i=1n1

=-x+ -a nn

=-x→-a

And, the mode of d1, d2, d3... dn will be -M-a

Also, we know that the variance σ2 is unaffected by change of origin, hence it remains same.

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About this question

This is a previous-year question from JEE Main 2014, 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.