Glen wrote:
>
> [EMAIL PROTECTED] (Tony) wrote in message news:<[EMAIL PROTECTED]>...
> > Hi,
> >
> > One of my collegues is working on a report to provide feedback to a
> > number of organisation that have provided data to us. One of these
> > statistics collected was how many weeks did it take to fill a vacancy.
> > In reporting this statistic back to the organisations my collegue
> > asked whether she should use the mean or the median. The reply from
> > her supervisor was "if the results are normally distributed then use
> > the mean otherwise use the median". I am sure this is sage advice,
> > but why?
>
> I would not call it sage advice. It depends on what you want to know.
>
> If interest centers on average time, then work with that.
> But beware! - note that if a vacancy remains
> unfilled you have a problem incorporating it in the average(since
> you don't know the number of weeks), and potentially an even bigger
> problem if you omit it (since it will generally be a large number of
> weeks that you know the number of weeks must exceed - so omitting it
> makes the average lower than it should be).
>
> (This is known as censoring. If the average is the desired quantity
> you'll need to make some assumption about distributional shape
> to estimate the average).
>
> It is possible that the median may be of greater interest in this
> case (in which case that's why you use it), and doesn't suffer from
> the censoring issue (unless the level of censoring is large).
>
> > I would have thought that if the distribution was normally
> > distributed then the mean and the median would be roughly similar
> > figures since the normal curve has the frequency distributed around
> > the mean.
>
> For any symmetric distribution whose mean exists, the population
> mean and median are the same. However, the sample median and the
> sample mean have different efficiencies (a more efficient estimator
> is able to get a better estimate of a quantity from a given sample).
> For example, for normal distributions and large samples, the median
> is about 64% as efficient as the mean (you need about 50% more
> observations to pin down the population mean as closely). And if
> the distribution isn't symmetric, the median will generally be biased
> for the mean - and generally, distributions are not symmetric.
>
> > My further thinking about this was that for any
> > distribution the mean will always be the upper bound of the median.
> > Is this correct?
>
> No. It will (depending on how you measure skewness), happen that
> for right skew distributions the population mean will be larger
> than the median, and the sample mean will usually follow suit.
>
> Glen
If you have Flash player 6, you can look my demo on the difference
between
the mean and the median from
http://noppa5.pc.helsinki.fi/koe/flash/mean/meanmedn.html
Juha
--
Juha Puranen
Department of Statistics
P.O.Box 54 (Unioninkatu 37), 00014 University of Helsinki, Finland
http://noppa5.pc.helsinki.fi
.
.
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