# Actual vs. Target

I’ve a data set contains two columns: actual value and target value. Is there a way where I can express the difference between these two columns as a single percentage value (that’s standardized, i.e., between 0-100%)? So I was wondering if I can calculate the standard deviation for the difference between values and then how can I standardize it to be a percentage between 0-100%?

Any help will be appreciated.

• It depends on what you mean by "difference as a percentage value" -- percentage of what, exactly? That is, what is it you want to measure? And, very much relatedly, what is it about the problem that makes it necessary that the error stay between 0 and 1 (100%)? Is the 'target' some kind of gold standard you want to measure the deviation from, or is it that you want to measure how far the target is relative to the actual? (And if you want either of those, how does that fit with the 0-1 restriction?) – Glen_b Jun 20 '13 at 21:18

mean(abs(a-t)/a) * 100

• This can exceed 100%. E.g., let the (target, actual) data be $((100, 100), (101, 1))$. Then $M = \frac{1}{2}\left(|\frac{100-100}{100}| + |\frac{1-101}{1}|\right)$ = $50$ = $5000$%. You might have been thinking of mean absolute relative percent difference, which does the trick provided all actual and target values are positive. (I'm not recommending this, though: in such cases, measures based on logarithms are better.) – whuber Jun 20 '13 at 18:49