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First post, let's hope you don't laugh.

I have a program that does 1,000 trials to calculate two values, a score and the std deviation of that score.

So now I have two columns of values

The first column ranges from about 1.4 to -0.8 and the second standard deviation column is generally between 0.08 and 0.3

I want to normalize scores to fall between 0 and 1. There are formulas on the net to do this and it's easy.

My question is, how can I also scale the stddev column in the exact same way so that I don't have to recalculate them?

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    I think the answer is just divide the stddev by the same denominator used in the score column. Can I have someone verify this is true?2012-02-02

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Let's suppose the first column $X_i$ has $\max_i(X_i)=1.4$ and $\min_i(X_i)=-0.8$. Then $Y_i = \dfrac{X_i-\min(X_i)}{\max(X_i)-\min(X_i) }= \dfrac{X_i+0.8}{2.2}$ is distributed in the range $[0,1].$

Let's call the terms of the second column $\sigma_{X_i}$. Then the same scaling will sugest you may want to have $\sigma_{Y_i} = \dfrac{\sigma_{X_i}}{\max(X_i)-\min(X_i) }= \dfrac{\sigma_{X_i}}{2.2}.$

You do not need to worry about the consistent translation in $X_i$: this does not affect the standard deviation. The standard deviation is proportion to a consistent scale factor.