If you would like to standardize your variable to mean zero and standard deviation one, I would suggest:

$s_{i} = \frac{x_{i}-c_{1}}{\sqrt{c_{2}-c_{1}^{2}}}$

where $x_{i}$ is your raw (not standardized) variable, $c_{1} = \sum_{i=1}^{N}x_{i}$ and $c_{2} = \sum_{i=1}^{N}x_{i}^{2}$.

That way, $s_{i}$ would have mean zero and standard deviation one. You could obviously leave away the standardization (standard deviation one) if you are not interested in that.

Is that what you are looking for?