On average and on the average are identical and mean the same thing. They are adverbial idioms and may appear first, last, or in most adverb niches.

Is it on average or an average?

The difference is that "On average" refers to the characteristics of the the group as a whole while "An average" or "The average" refers to a typical, representative, member of the group.

Is it correct to say on average?

You say on average or on an average to indicate that a number is the average of several numbers. American shares rose, on average, by 38%. On an average we would be spending £200 per day.