The average of the squares of the natural numbers from 1 to 11 is _________.

The formula for the sum of the squares of the first n natural numbers is:
Sum=
6
n(n+1)(2n+1)
​

The average of the squares of the first n natural numbers is:

Average=
n
Sum
​
=
6
(n+1)(2n+1)
​

Given n=11:

Average=
6
(11+1)(2×11+1)
​

Average=
6
12×23
​

Average=2×23=46