In some versions of numpy there is another important difference that you must be aware:
average does not take into account masks, so compute the average over the whole set of data.
mean takes in account masks, so compute the mean only over unmasked values.
g = [1,2,3,55,66,77]
f = np.ma.masked_greater(g,5)
np.average(f)
Out: 34.0
np.mean(f)
Out: 2.0