# Re: Idempotence and "Replication Insensitivity" are equivalent ?

Date: 25 Sep 2006 00:58:58 -0700

Message-ID: <1159171138.596078.240390_at_e3g2000cwe.googlegroups.com>

Phil Carmody ha scritto:

> "Brian Selzer" <brian_at_selzer-software.com> writes:

*> > You wrote, "There are some sets, such as {0, 1}, where every value between 0
**> > and 1 (including both endpoints) is minimum."
**> >
**> > Unless 0 and 1 belong to some domain other than integers, whole numbers or
**> > real numbers, it is clear that 0 is the minimum value of the set {0, 1}.
**>
**> Nope, what was said in its correct context was this:
**>
*

Are you guys reading the posts or just interested on fighting? I have already admitted on a post that Google shows with number 159...

"So the median does have an optimality property similar to the mean. But in order to make this property a "characterizing" one, the assumption is made that, for even cardinalities, the average of the 2 (n>1) central terms is to be taken. In fact, as Phil noted - in case n is even - all points between the 2 central terms (end point included) are point of minimum for the sum of absolute deviations, as clearly they are contained in all the intervals of type x(i) - x(n-i+1), i=0,...,n\2. "

...that Phil statement about each point of the central interval being a minimum. What I think he was wrong about is that (perhaps) he believed that the result could depend on some numerical "domain", although he did not explain what he meant by "domain". If he meant the value type within numerical types, such as integer, single, double, the statement is not true. If he means the "kind" of data, that can be true, as for qualitative data the median definition is to be adjusted, as the average of the 2 central terms clearly does not exist. So in case n is even (2*i) both the central terms are taken. If they coincide there is no problem. If they differ, then we have 2 median values (qualitative).

-P Received on Mon Sep 25 2006 - 09:58:58 CEST