On Sat, 2007-10-02 at 02:41 +0200, Leonard Mada wrote: > John Machin wrote: > > ... > > So who cares? The median value is 1. Is your alternative going to > > return some value other than 1 ???? > > Please define mathematically the middle value! It is NOT trivial as my > definitions showed. Anything else would be ambiguous. This should be a > standard, so make a better definition.
Contrary to your claims, there is nothing ambiguous. Any non-decreasing list of the same values has the same middle value(s). > > Well, I could have used a much shorter definition: the median is the > value that halves the list so that there are two sets of equal size with > numbers in the first set being higher than the median and numbers in the > second set being lower. As noted, this definition avoids the sorting, > too. (One could extend this definition for even and odd number of > elements. Or even a much shorter definition: the 50th percentile. BUT > all these definitions are ambiguous, see later.) > > The one thing that I do NOT agree at all with the OASIS definition is, > that it includes the wording "sorting". Sorting is definitely NOT > necessary to calculate the median. You can take any array, even one that > is NOT sorted, and determine the median without first sorting it. This > is much to often stated wrongly in so many textbooks, BUT sorting is > really not necessary. The OpenFormula standard does not prescribe any method used to find the value. It only prescribes what the value is. > > So, this is NOT a prerequisite that should enter a standard definition. > > May I even point out, that for even number of elements, one may > define/have an upper median and a lower median. Alternatively, in > serious mathematical uses, the median is usually calculated using a > weighted approach. Therefore, the median of 1,2,2,3,4,5 is NOT (2+3)/2 = > 2.5, BUT rather (2+2+3)/3 = 2.66. So, it does make sense to have a very > strong and unambiguous definition in a standard. > The *weighted median* may be introduced later into the standard and then > the ambiguity would be complete. MEDIAN is not intended to implement a weighted median. None of the current spreadsheet implementation uses that name for a weighted median. Gnumeric for example does also provide a function for a weighted median, namely SSMEDIAN. That function may at some time also be introduced in the Standard but would in no way make other definition ambiguous. Andreas -- Prof. Dr. Andreas J. Guelzow Dept. of Mathematical & Computing Sciences Concordia University College of Alberta _______________________________________________ gnumeric-list mailing list [email protected] http://mail.gnome.org/mailman/listinfo/gnumeric-list
