JEE Main 2019MathematicsStatisticsMediumMCQ

JEE Main 2019 — Statistics Question with Solution

JEE Main 2019 (10 Apr Shift 2)

Question

If both the mean and the standard deviation of 50 observations x1, x2, …, x50 are equal to 16, then the mean of x1-42, x2-42, …,x50-42 is

Choose an option

Show full solutionCorrect option: C
Correct answer
C400

Step-by-step explanation

For observations x1, x2, ...........x50

We have, mean, x¯=∑xi 50=16   .....i

And, standard deviation, σ=∑xi250-x¯2=16

⇒∑xi250=162+x¯2

⇒∑xi250=162+162=512  .....ii

Now, the mean value of x1-42, x2-42, ..., x50-42 will be

=∑xi-4250=∑xi2-8 ∑xi+16×5050

=∑xi250-8∑xi50+16

 Using i and ii,

=512-8×16+16=400.

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About this question

This is a previous-year question from JEE Main 2019, 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.