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George, I'm not sure whether I understand your concerns:

> But starting with a normal distribution, the resulting scatter in the
> median is significantly greater than the scatter in the mean, simply
> because so much of the numerical information has been discarded. So Marcel
> is paying a heavy price. I wonder if he has made an analysis of any
> benefits of this procedure.

For any symmetrical distribution mean, median and mode are identical.
If you have good reason to believe that the measured data are expected
to be symmetrically distributed, the median can be used. A
considerable difference between mean and median indicates either the
existance of outliers or a the possible existance of a skew
distribution. In "normal" datasets there is no a great difference
between the mean and the median. In small datasets an outlier
contributes too much. One outlier within e.g. 6 data contributes 17%
(if not weighted) whereas the outlier may in reality have a much lower
probability. The median thus helps to "correct" the influence of
outliers in small datasets.

Marcel

   

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