There are several types of mean. When most people talk about an average, they are usually referring to the arithmetic mean (the sum of values in a set divided by the number of values).

However there are also other means (e.g. where relationships are multiplicative rather than additive)such as the geometric or harmonic mean. So,in economic statistics, if you wanted to find the average of several index numbers, you would use the geometric mean. For example, the (geometric) mean of two index numbers is the square root of their product.

In an everyday context, average and mean are more or less interchangeable. But if it is a specialist text it is worth checking to see what type of mean is being used, so that people do not automatically assume that it is an arithmetic mean. In short moyenne needs an adjective!

geometric mean: the nth root of the product of n numbers; specifically : a number that is the second term of three consecutive terms of a geometric progression <the geometric mean of 9 and 4 is 6>
arithmetic mean: a value that is computed by dividing the sum of a set of terms by the number of terms
average: 1 a : a single value (as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values b : MEAN 1b
2 a : an estimation of or approximation to an arithmetic mean b : a level (as of intelligence) typical of a group, class, or series <above the average>
3 : a ratio expressing the average performance especially of an athletic team or an athlete computed according to the number of opportunities for successful performance

The use of one or the other will depend on the type of text you are translating.