Tell me the definition of average, as in an average value calculated from a set of numbers. Ex: The average height of a population.

Do not tell me how to calculate an average. Tell me what it MEANS. Try as I might, I have only found one source on the internet after 10 minutes of searching that defines what an average is instead of how to calculate an average, but it's a definition of philosophy.

Example: A quick google search for "definition of average" brings up the following definition:

the result obtained by adding several quantities together and then dividing this total by the number of quantities; the mean.

This is not the definition of what average is, it only tells you how to find it.

I already have two real definitions of what average is, one my own and one from my old junior high math teacher from many years ago.

EDIT: Good job with the definitions. I like having thought-provoking discussions that dabble a little bit in philosophy.

The old definition from my junior high math teacher (as best I can remember it) is as follows: "A number that reflects the entire group of numbers if they were all exactly the same." I never really cared that much for this definition, but seeing as how the it came from a highly educated math teacher that served on U.S. nuclear submarines I've always respected it.

My own definition is this: (Mathematical) average is a number that is most probably representative of a given range of values in a group of numbers (or data set).

Double Edit: It was pointed out to me that I should specify, at least for the mathematical definition of average, I am referring to mean average. Median and mode average are different.

Here's a sexy McLaren F1 butt for your troubles:

Challenge for all you Opponauts out there: Edit: Challenge complete