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Topic: Is this mathematically possible?
Replies: 16   Last Post: Oct 18, 2010 4:34 PM

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Snidely

Posts: 9
Registered: 10/15/10
Re: Is this mathematically possible?
Posted: Oct 18, 2010 4:34 PM
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On Oct 18, 12:25 pm, "()" <karom...@yahoo.com> wrote:
> On Oct 15, 10:09 pm, Snidely <snidely....@gmail.com> wrote:
>
>
>

> > On Oct 15, 1:03 pm, "()" <karom...@yahoo.com> wrote:
>
> > > On Oct 15, 6:46 pm, Snidely <snidely....@gmail.com> wrote:
>
> > > > On Oct 15, 1:18 am, Jared <jared4...@gmail.com> wrote:
>
> > > > > Let's say you are given a mean and a median for several percentile
> > > > > ranges.

>
> > > > > From the zeroth to the 20th percentile, let's say the median is 7.5
> > > > > and the mean is 72.6.
> > > > > From the 20th to the 40th percentile, the median is 33.7 and the mean
> > > > > is 121.5.
> > > > > And from the 40th to the 60th percentile, the median is 72 and the
> > > > > mean is 194.6.

>
> > > > > The rest doesn't really matter; this illustrates my point.
>
> > > > > How can the mean for 0-20 be higher than the median for the 40-60
> > > > > range? Isn't that mathematically impossible?

>
> > > > I am having trouble picturing what is being described here.  A median
> > > > of 7.5 and a mean of 72.6?  An order of magnitude difference?  That
> > > > sounds like very skewed data, which I suppose is possible if you're
> > > > looking, for example, at a gaussian distribution from the tail to
> > > > where the central bump just takes off (steeply).  

>
> > > Just one outlier can skew the mean.  7.3, 7.5 and 203 have median 7.5
> > > and mean 72.6.

>
> > The outlier should be in a different percentile range, shouldn't it?
>
> It is only an outlier within its percentile range. The numbers were
> just to illustrate with a concrete example how a set of numbers could
> have given the median and the mean. Another possibility would be if
> the numbers were from a distribution with a large standard deviation,
> say 1000, then the difference between 7.5 and 72.6 is hardly
> significant (in the non-statistical sense).


It's true that we don't know the distribution the OP was referring
to, but 203 should be out of the percentile range that 7.5 falls in,
since the next median 33.7, implying the range boundary is between 7.5
and 33.7.

/dps




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