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Question

# Assertion :The variance of first n natural numbers is n2âˆ’16 Reason: The sum and the sum of squares of first n natural numbers are n(n+1)2 and n(n+1)(2n+1)6 respectively.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

## The correct option is D Assertion is incorrect but Reason is correctFirst n natural numbers are, 1,2,3,..........nHere ∑xi=n(n+1)2,∑x2i=n(n+1)(2n+1)6Ergo variance is σ2=∑x2in−(∑xin)2=n2−112Clearly Assertion is incorrect, obviously Reason is correct.

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