Re: Median --- what good is it?

Am 14.08.05 03:56 schrieb ediebur@xxxxxxx:
> I saw "median" used yet again in the context of the number of weeks
> unemployed. What real use is the median? What does it really tell us? I
> was exposed to stats as part of an applied math major and except for
> the definition, it was never discussed in the stats courses I took ( 2
> or 3).
>
a) while the mean is the value m, which is optimal in the sense of
minimizing quadratic deviations from m, the median is the value m,
which is optimal in the sense of minimizing absolute deviations
from m.
A consequence of this is that outliers are less influential in
the median since quadratic deviations grow faster than absolute
deviations.

b) It has conceptual consequences for our way, how to view a
-for instance- sociological problem and describe a relevant
central tendency.

Assume a village of 100 people having monthly income of ~$2000 each.
The mean as well as the median is ~ $2000
Now a really rich person is moving to that village, he has $200 000
each month.

If we describe the village in terms of the mean, then the average
income has changed to $400 000/101 ~ 4000$ , but the median is
still about ~$2000.

Now it depends, for which purpose we use the central tendency.
The mean of ~ $4000 may be of interest as average money, if you
count the coins, or do some banking or tax management which deals
with linear functions of the money present in the village.

The median of ~$2000 is of more interest, if we describe some
social parameter, like the ability of the people of that village
to share some cultural affairs, pay for education etc, which has
not changed with the new powerful inhabitant (but would, if, let's
say 50 people of that high income would move to that village: then
33% of the inhabitants are very powerful, and then the social
characteristic of that village had really changed)

Gottfried Helms
.

Relevant Pages

  • Bourne Shell Script Newbie Help
    ... I need some assistance in starting an assignment. ... Your script will be called stats. ... The option -rows calculates the average and median across the ... output an error message to standard error. ...
    (comp.unix.shell)
  • Re: Whale steak
    ... intended is mean, mode or median. ... Inger did not so specify. ... I've only had some stats courses, ...
    (sci.archaeology)
  • Re: Whale steak
    ... intended is mean, mode or median. ... I've only had some stats courses, ... aimed at pure mathematics, engineering mathematics and psychology. ...
    (sci.archaeology)
  • Re: Whale steak
    ... intended is mean, mode or median. ... I've only had some stats courses, ... And Inger used medium to mean what? ... "Pupils produce a poster explaining when they should use each of the ...
    (sci.archaeology)