I'm looking for a formula to show deviations from zero. I have a data set with values that that is normalized to positive real numbers where zero is perfect and higher is worse. I need a statistical formula that gives me a number over the whole set. I'm now using standard deviation, and it is showing me some interesting results, but as I understand standard deviation normalizes on the average of the set. I need it to use zero as the basis.

  • $\begingroup$ If your positive numbers are $x_1, \dots, x_n$ then you can use something like $\sqrt{\frac{1}{n}\sum x_i^2}$? $\endgroup$ – kjetil b halvorsen Nov 14 '13 at 16:24
  • $\begingroup$ My math abilities are nowhere close enough to be able to understand this. Can you give me a WikiPedia page or a layman's explanation of this formula, maybe as an answer :). $\endgroup$ – Pieter van Ginkel Nov 15 '13 at 9:28
  • $\begingroup$ That formula is the standard deviation, but around zero, not around the average ... $\endgroup$ – kjetil b halvorsen Nov 16 '13 at 9:56
  • $\begingroup$ Thanks. I've applied it (someone helped :) ) and it looks just fine. If you make it an answer, I can accept it. $\endgroup$ – Pieter van Ginkel Nov 16 '13 at 20:59

If you want to measure deviations from zero, you can just use the standard deviation around zero, and not around the average. The formula will be: $$ \sqrt{\frac{1}{n}\sum_{i=1}^n x_i^2} $$


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