----- Original Message -----
From: David A. Heiser <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>; Glen Barnett <[EMAIL PROTECTED]>
Sent: Friday, September 01, 2000 1:13 PM
Subject: Re: Skewness and Kurtosis Questions
> Barnett then goes on...
>
> > > Now, if I delete the two 150's on the end of data set #1 and change the
> > > ranges on the formulae, I get a mean of 7.28 and I still get a median of
> 0.
> > > Again, the mean is larger than the median so this should be positively
> > > skewed but Excel returns a value of -0.370.
> >
> > It looks like you've just constructed just such an example as I mentioned.
> >
> > > I have verified Excel's calculations manually and they appear to be
> correct
> > > so it would appear that the commonly used statement that:
> > >
> > > mean > median: positive, or right-skewness
> > > mean = median: symmetry, or zero-skewness
> > > mean < median: negative, or left-skewness
> > >
> > > is incorrect, or, am I overlooking something?
> >
> >It is correct if you measure skewness in terms of mean-median. If you
> >measure it some other way, it is no longer true. Note in particular
> >that zero third central moment does not imply symmetry (contrary
> >to what some books assert).
>
> If you use form 1) or form 3) then a zero value represents complete
> symmetry.
(I snipped them, but both forms were moment/cumulant based
measures)
I'm sorry, but this is wrong.
Counterexamples are easy to construct and can be found
in the literature. You can even set *all* odd moments to zero
and still have non-symmetry. See, for example, Kendall and Stuart.
Glen
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