On Tue, 14 Mar 2017 09:14:45 +0200 Serhiy Storchaka <storch...@gmail.com> wrote: > The median tells you that results of a half of runs will be less than > the median and results of other half will be larger. This is pretty > informative and even more informative than the mean for some > applications.
How so? Whether a measurement is below or above the median is a pointless piece of information in itself, because you don't know by how much. If a sample is 0.05% below the median, it might just as well be 0.05% above for all I care. If half of the samples are 1% below the median and half of the samples are 50% above, it's not the same thing at all as if half of the samples are 50% below and half of the samples are 1% above. Yet "median +/- MAD" gives the exact same results in both cases. > > Additionally, while mean and std dev are generally quite well > > understood, the properties of the median absolute deviation are > > generally little known. > > Std dev is well understood for the distribution close to normal. But > when the distribution is too skewed or multimodal (as in your quick > example) common assumptions (that 2/3 of samples are in the range of the > std dev, 95% of samples are in the range of two std devs, 99% of samples > are in the range of three std devs) are no longer valid. Not for individual samples, but for expected performance over a large enough number of runs, yes, you can more or less use common assumptions (thanks to the central limit theorem). And expected performance is a rather important piece of information. Regards Antoine. _______________________________________________ Speed mailing list Speed@python.org https://mail.python.org/mailman/listinfo/speed
