JEE Main 2014MathematicsStatisticsEasyMCQ

JEE Main 2014 — Statistics Question with Solution

JEE Main 2014 (06 Apr)

Question

The variance of the first 50 even natural numbers is :

Choose an option

Show full solutionCorrect option: D
Correct answer
D 8 3 3

Step-by-step explanation

Variance of a set of n numbers x1, x2 ...xi, ...xn is given

σ2=1nΣi= 1nxi-x¯2, where x¯ is the average of the numbers.

We want the variance of 2, 4, 6, 8 ..... 48, 50, 52, ..... 98, 100

Here x¯=51.

xi-x¯ will be symmetric about 51,

∴σ2=25012+32+52+... 492

Now, 12 + 32 + 52 + ... + 492 = 12 + 22 + 32 + ... + 492 + 502 - 22 + 42 + 62 + ... + 482 + 502

=50511016-412+22+

=50511016-42526516

 = 42925 - 22100

 = 20825

∴σ2=250×20825=833

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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.