On Mon, 28 Aug 2000, Ronny Richardson wrote:
> Several references I have looked at define skewness as follows:
>
> mean > median: positive, or right-skewness
> mean = median: symmetry, or zero-skewness
> mean < median: negative, or left-skewness
He then gave two small (N = 20) discrete examples for which these
statements did not hold, and asked plaintively,
> ... Why should a mean and median that are closer together generate a
> skewness measure that is so much larger? Does this mean that the
> magnitude of the skewness number has no meaning?
< snip >
> 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?
As with rules of thumb generally, there are implied conditions. The
statements you quote are more or less general summaries of what one
often finds with continuous unimodal distributions, and with discrete
distributions that are reasonably well-behaved. Anyone can, with a
little thought, devise pathological discrete distributions for which
general statements like these are not true. Your pathological
distributions, in particular, are heavy-tailed at one or both ends and
the first one is multimodal (and otherwise badly behaved).
Do read the papers offered by Karl Wuensch and David Heiser.
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
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