Re: BASIC Q: Why not use median-based std deviation?
From: Richard Ulrich (Rich.Ulrich_at_comcast.net)
Date: 07/09/04
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Date: Thu, 08 Jul 2004 22:23:26 -0400
On Thu, 8 Jul 2004 21:41:37 +0000 (UTC), wolfhart13@yahoo.com
(William) wrote:
> Since the median (unlike the mean) is skew-resistant, why not use it
> instead of the mean in calculating the standard deviation?
>
> I know there's a perfectly logical explanation why only the mean is
> used, but for the life of me can't figure out why the median could not
> also be used, especially in highly skewed distributions.
>
> Can someone shed some light on this?
The SD is the average second central moment.
As such, it has an enormous role as a *parameter*
of distributions and test statistics.
The mean, similarly, is much more often an actual
*parameter* of a distribution that we find useful,
compared to the median.
The median is occasionally used, for specific gains,
and there are books on 'robust statistics' that
use the median and (often) its natural counterpart
(since it is at its minimum around the median), the
absolute deviation.
-- Rich Ulrich, wpilib@pitt.edu http://www.pitt.edu/~wpilib/index.html
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