I am assigning values to objects in a process. I would like the values to end up being normally distributed with variance one. For this I standardise them by subtracting their average from each and dividing by the standard deviation. Thus they end up with "normal" mean and variance. But they tend to have a large skewness. I can calculate their skewness, but what do I do with it? What operation is necessary to apply to the values with regard to skewness so that they are not skewed? (I am guessing it is either logarithm or root.)
EDIT: I am looking for a formula to apply to the values that takes the skewness into account and makes it zero.
If a random variable $X$ has a continuous cumulative distribution function $F$, you can transform it into $f(X) \sim \mathcal{N}(0,1)$ by considering $f(x)=\Phi^{-1} \circ F(x)$, where $\Phi$ is the cumulative distribution function of a standard normal distribution. See here for details. Of course, in practice $F$ is not known, but you can replace it by the empirical cumulative distibution function $\widehat{F}$. Then $\widehat{F}(X_{(1)})=1/n$ for the smallest value $X_{(1)}$ in your sample, $\widehat{F}(X_{(2)})=2/n$ for the second smallest value $X_{(2)}$, etc. (note that if you do this, you will have to discard the largest value in your sample because $\Phi^{-1}(1)$ is not defined or would be $+\infty$).