this is my first question, so please don't be too harsh on me. In order to simplify a standard deviation i have managed to isolate some terms. I'm however unsure of how i can rewrite or simply calculate the term $\sum_{i=1}^n x_i * x_i$ given that i know $\sum_{i=1}^n x_i$ and $n$. $\sum_{i=1}^n x_i * x_i \neq 2*\sum_{i=1}^n x_i$, right?
The problem is that i do not know $x_1 ... x_i$ but just the two things. Can it be computed? Any help appreciated, thanks alot.
The sum of squares is a separate quantity from the sum. Knowing the sum
$$\sum_{j=1}^n x_j$$
doesn't help you figure out the sum of squares
$$\sum_{j=1}^n x_j^2.$$
If your $x_j$ are large in magnitude, like $(-100, 200, 100, 0, -200)$, then the sum of squares will be big. If they're smaller, like $(18, -22, 0, 22, -18)$, the sum of squares will be less. If they're all zero, like $(0, 0, 0, 0, 0)$, then the sum of squares will be zero.
But note that all three of these sets have five elements, and a sum of zero.
The only way to figure out the sum of squares from what you're given is to compute it directly.