Question

Variance of first 2n natural numbers?

Answer 1

To find the mean and variance of n natural numbers:

Step 1: Mean The sum of n natural numbers is given by $\frac{2n(n+1)}{2}$.
Therefore, the mean is $2n+1$.
Step 2: Variance
The variance can be calculated using the formula $(6n(n+1)(2n+1) - \frac{(2n+1)^2)}{(2(n+1))}$.
Simplifying further, it becomes $\frac{(12n^2 - 1)}{(2n+1)}$.

Hence, the correct option for the variance is $\frac{(12n^2 - 1)}{(2n+1)}$.