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 \(\frac{(12n^2 - 1)}{(2n+1)}\).