Statement 1 : variance of first n odd natural numbers is frac{{{n^2} - 1}}{3} Statement 2 : su

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13.Statistics

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Statement $1$ : The variance of first $n$ odd natural numbers is $\frac{{{n^2} - 1}}{3}$
Statement $2$ : The sum of first $n$ odd natural number is $n^2$ and the sum of square of first $n$ odd natural numbers is $\frac{{n\left( {4{n^2} + 1} \right)}}{3}$

A

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

B

Statement $1$ is true, Statement $2$ is true;
Statement $2$ is not a correct explanation for Statement $1$.

C

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

D

Statement $1$ is true, Statement $2$ is true,
Statement $2$ is a correct explanation for Statement $1$.

(AIEEE-2012)

Solution

Statement $2$ : Sum of first $n$ odd natural numbers is not equal to $n^2$ So, statement $- 2$ is false.

Standard 11

Mathematics

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