Statement-1 : The variance of first n even natural numbers is

Question:

Statement-1 : The variance of first $n$ even natural numbers is $\frac{n^{2}-1}{4}$

Statement-2 : The sum of first n natural numbers is $\frac{n(n+1)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{6}$.

  1. Statement–1 is true, Statement–2 is false.

  2.  Statement–1 is false, Statement–2 is true.

  3. Statement–1 is true, Statement–2 is true ; Statement–2 is a correct explanation for Statement–1. 

  4. Statement–1 is true, Statement–2 is true ; Statement–2 is not a correct explanation for statement–1. 

Correct Option: , 2

Solution:

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