# About the resolution/$\sqrt{12}$ uncertainty

Suppose you want to measure a (real-valued) quantity with an apparatus which will return as a result of the measurement the closest integer to the true value of the quantity.

Then, a common use is to quote an uncertainty of +/- $1/\sqrt{12}$ (which, as a matter of fact, is the standard deviation of a uniform distribution of width 1. Let's note that this interval does not correspond to 68% probability)

Now, my question is : where does this value come from ? Is this "quantization" error treated as a systematic ? (and therefore the resolution/$\sqrt{12}$ factor would just be a rather subjective estimate of it ?)

Is your question why the error distribution is a uiform distribution with width 1 or why this distribtution has a standard deviation of $1/\sqrt{12}$? –  jkej Apr 2 '13 at 14:37