Means and extremes in classical mathematics have to do with proportions.
If A is to B as C is to D, we write A : B :: C : D. This is ordered so that A is greater than or equal to B and C is greater than or equal to D. A and D are called the extremes; B and C are called the means.
By elementary algebra the product of the extremes equals the product of the means:
A x D = B x C.
If B = C, then B is the mean proportional or geometric mean of A and D. In that case B is the positive square root of A x D.
This provides a basic principle for centrism: the means are between the extremes in a principled manner.