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

From: vc <boston103_at_hotmail.com>
Date: 25 Sep 2006 06:29:18 -0700

pamelafluente_at_libero.it wrote:
> vc ha scritto:
>
>
> > My point sumply was that neither the minimizing property, nor any
> > other median definition defines the median uniquely in certain cases.
> >
>
> Let me clarify this point.
[...]
> 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.

>
> 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 - 15:29:18 CEST

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