Question

The mean of the following data $1^2,2^2,3^2,4^2,........n^2$ is ______.

• A. $\frac{(n+1)(2n+1)}{6}$
• B. $\frac{n(n-1)(2n+1)}{6}$
• C. $\frac{n(n+1)(2n-1)}{6}$
• D. $\frac{n(n-1)(2n-1)}{6}$

Answer 1

The correct option is A

$\frac{(n+1)(2n+1)}{6}$

The sum of the squares of the first n natural numbers is $\frac{n(n+1)(2n+1)}{6}$.
The mean is the sum divided by the number of terms. Therefore, the mean is

$\frac{\frac{n(n+1)(2n+1)}{6}}{n}=\frac{(n+1)(2n+1)}{6}$