Statement 1: The variance of first n odd natural numbers is (n2-1/3) Statement 2: The sum of first n odd natural number is n2 and the sum of square of first n odd natural numbers is (n(4n2-1)/3).

Question

Statement 1: The variance of first n odd natural numbers is (n2-1/3) Statement 2: The sum of first n odd natural number is n2 and the sum of square of first n odd natural numbers is (n(4n2-1)/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.

Tardigrade Admin · Accepted Answer

Statement 2: Sum of first n odd natural numbers is not equal to n2. So, statement - 2 is false.

Q. 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 $\frac{n ( 4 n ^{2} - 1 )}{3} .$

Statement 1 is true, Statement 2 is false.

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

Statement 1 is false, Statement 2 is true.

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

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

Q. Statement 1 : The variance of first n odd natural numbers is 3n2−1​ Statement 2: The sum of first n odd natural number is n2 and the sum of square of first n odd natural numbers is 3n(4n2−1)​.