Imagine f(X) is some function (transform) of X, and g(X) is another function

(transform) such that X = g(f(X)) (i.e., g(X) reverses or undoes what f(X)

did to X). We could then define some new kind of mean of X in general as:

X= g(∑f(X) / N)

what type of mean fits with this data(absolute mean, root-mean squared, geometric mean, or harmonic mean) and why?

my guess was geometric mean...but i dont really know