So I am trying to derive the following relation using Cauchy Schwarz inequality for any collection of N real numbers:

This says that the square of the average is less or equal than the average of the squares.

So I want to use to derive this.

So needs to be therefore, I have as and as providing that:

{1}{N}" alt="{1}{N}" />

Am I going in the right direction? Can anyone provide me some guidance?