On 11 Apr, 21:29, Gabriel Genellina <[EMAIL PROTECTED]> wrote: > ... If the numbers to be rounded come from a > measurement, the left column is not just a number but the representant > of an interval (as Mikael said, the're quantized). 2.3 means that the > measurement was closer to 2.3 than to 2.2 or 2.4 - that is, [2.25, > 2.35) (it doesn't really matter which side is open or closed). It is > this "interval" behavior that forces the "round-to-even-on-halves" > rule. > So, the numbers 1.6-2.4 on the left column cover the interval [1.55, > 2.45) and there is no doubt that they should be rounded to 2.0 because > all of them are closer to 2.0 than to any other integer. Similarly > [2.55, 3.45) are all rounded to 3. > But what to do with [2.45, 2.55), the interval represented by 2.5? We > can assume a uniform distribution here even if the whole distribution > is not (because we're talking of the smallest measurable range). So > half of the time the "true value" would have been < 2.5, and we should > round to 2. And half of the time it's > 2.5 and we should round to 3. > Rounding always to 3 introduces a certain bias in the process. > Rounding randomly (tossing a coin, by example) would be fair, but > people usually prefer more deterministic approaches. If the number of > intervals is not so small, the "round even" rule provides a way to > choose from that two possibilities with equal probability. > So when we round 2.5 we are actually rounding an interval which could > be equally be rounded to 2 or to 3, and the same for 3.5, 4.5 etc. If > the number of such intervals is big, choosing the even number helps to > make as many rounds up as rounds down. > If the number of such intervals is small, *any* apriori rule will > introduce a bias.
Great explanation! -- Arnaud -- http://mail.python.org/mailman/listinfo/python-list