Lets say that for every city the height of the population is measured. Every city would have a different mean, and the average mean would be the average of the means of each city. In statistics, every trial has a mean, and the average mean would be the average of the means over each trial. The average mean is almost always normally distributed, and has properties which depend on the number of trials. Here, each trial is the height survey of each city, and the average mean would be the national average of height, which is measured by taking the average of all the height means of each city.

"Average" and "Mean" are normally two terms used for the same expression, namely the sum of all elements divided by their number. Using both of these terms is normally done to clarify which form of a mean we choose among quite a few options as there are several other ways to find a mean of a set of values (median, geometric mean, ...). It should correctly be called "arithmetic mean".

For example, if i have four values 1,5,6 and 8, i sum them up, which would be 1+5+6+8 = 20 and then divide by the number of values, which is four. So the average mean would be 20/4 =5.