# Re: Median: Oasis and Fast Sorting Algorithm

*From*: Leonard Mada <discoleo gmx net>
*To*: gnumeric-list gnome org
*Subject*: Re: Median: Oasis and Fast Sorting Algorithm
*Date*: Sat, 10 Feb 2007 02:41:55 +0200

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.
`

`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.
`
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. So, let's do a good job now and not
``when it is too late.
`
Leonard

[

Date Prev][

Date Next] [

Thread Prev][

Thread Next]
[

Thread Index]
[

Date Index]
[

Author Index]