On Jan 25, 2014, at 12:46 PM, Donald Sauter <email@example.com> wrote:
> I thought my example disproved that. Doesn't the word "skewed" imply an extra-mathematical judgment imposed on simple numbers? When we say "skewed data," doesn't that imply, "Even though this is the _raw_ data, we know that it's _really_ trying to say such and such"? > > I am not touching that situation. I am only addressing the problem, given a bunch of raw data for which you do not have "insider information", what is the best "measure of central tendency"? If you know the answer you want, and the median happens to hit closest, go ahead and trumpet the median. But that's not math.
It is math. For example, if I were to choose 10 houses at random and take the ?mean? price of those 10 houses, would it be closer to the ?median? price of all houses, or the ?mean? price of all houses?
The ?median? gives a better ?probable" mean than the ?mean? when the data is skewed. That is often more useful than the mean of all houses.
If you want to go beyond trying to argue what is the ?best? metric, then the raw data itself is the only real metric.