Re: Median --- what good is it?



Randy Poe wrote:
|Median captures our sense of "average" a lot better when
|distributions are very skewed, such as in salary or housing
|price distributions.

I would say "typical" rather than "average". The average
captures the sense of average.

There was a good example of the pitfalls of averaging.
Some propagandists circulated the claim that the "average"
American family pays more in taxes than on food, clothing,
and shelter. There were a few things wrong with this.
For one thing, they were counting taxes on dividends as
taxes but not counting dividends as income. Probably worse,
they were averaging not the proportion of income spent on
these things, but the amount spent, so that a family having
twice the income gets weighted as much in the average as
two families having half. This causes the situation for the
highest income families (who tend to spend a relatively
small fraction of their incomes on food, clothing, and
shelter, and a somewhat higher fraction on average on taxes)
to be "averaged" into the mix with a heavy weight.

In fact, a majority of American families spend over half
of their income on food, clothing, and shelter, certainly
more than what we spend on taxes. The median figures bear
this out.

Keith Ramsay

.



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