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

From: <pamelafluente_at_libero.it>
Date: 25 Sep 2006 07:06:27 -0700

vc ha scritto:
> [...]
> > In order to have a unique solution (and therefore equivalence), in the
> > case we are dealing with finite set of numbers when the cardinality is
> > not odd, the definition of MEDIAN is "completed" by *assuming* (it's
> > an ASSUMPTION, a convention) as median the average of the 2 central
> > terms of the ordered sequence of numbers:
> >
> > MEDIAN = ( x(n\2) + x(n\2 + 1) ) / 2
>
> The convention, while convenient in many cases, does not work if we
> want to preserve invariance to monotonic transformations. Considering
> the entire interval as the median is the only way to preserve the
> invariance property.

I have simply recalled the standard definition, but I have some "feeling" that this can be an interesting point.

Can you make an example of what you have exactly in mind? Stated so generally it's not clear (to me) what you are referring to. Invariance is sometimes used with different meanings, eg, in the case of the variance we say that it is translation-invariant.
What kind of "invariance" have you in mind ?

-P

>
> >
> > for n odd there is no problem, as the median is the central term
> > x((n+1)\2) .
> >
> > For qualitative data is a different story...
> >
> > -P
Received on Mon Sep 25 2006 - 16:06:27 CEST

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