There are a couple of (practical) features of the standard deviation that are
worth noting.
First, as a *descriptor* of the variation in a distribution, it is generally not
very good. I mean this is the sense that if you want to visualise the amount of
variation in a distribution the SD is only useful if the distribution is at
leasst symmetric and preferably approximately normal. This appears to me to
contribute to the difficulty that students have with it.
Second, for a normal distribution, it is easily seen that the variatiion can be
described (and measured) by the 'width of the peak'. The question is, at what
point do we measure the width? Geometrically, the only two uniquely identifiable
points on the curve, other than the maximum, are the two inflexions. (I usually
describe these to students by getting them to imagine they are ants riding a
motor bike along the curve; they lean into the curve one way, then straighten up
and lean the other way.....) Consequently, the only measure of the width of the
peak that makes sense is the distance between these points - and this is twice
the standard deviation. Hence (I think) the word 'standard'.
Regards,
Alan
Herman Rubin wrote:
> In article <[EMAIL PROTECTED]>,
> Neil <[EMAIL PROTECTED]> wrote:
> >I was wondering what the standard deviation means exactly?
> I believe the reason it is called the STANDARD deviation
> is that if the probability distribution is concentrated
> equally at the two points one standard deviation from
> the mean, the first two moments agree with that of the
> original distribution; the deviation from the mean to
> get this is the standard deviation.
> --
--
Alan McLean ([EMAIL PROTECTED])
Department of Econometrics and Business Statistics
Monash University, Caulfield Campus, Melbourne
Tel: +61 03 9903 2102 Fax: +61 03 9903 2007
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