There are many other interesting types of averages as well! For example (using only 2 numbers for simplicity) the p-mean of x and y (assumed to both be positive) is defined as ((x^p + y^p)/2)^(1/p), the pth root of the average of the pth powers of x and y. Here p can be any number except 0, even if it is not an integer. For p = 1 this is the ordinary average. For p = 2 it's called the root-mean-square, which is used to find the "standard deviation" of a bunch of numbers. For p = -1 it's called the "harmonic mean".

Another kind of mean is the "geometric mean": the square root of the product of x and y. Interestingly, this turns out to be the limit of the p-mean of x and y as p approaches 0. Puzzle for the reader: What happens to the p-mean of x and y as p approaches infinity? What happens to the p-mean as p approaches negative infinity?

PS I would not call the "range" a method of averaging. It is a useful statistic, but an average it is not.