I have a graduate education in probability and statistics; in the technical literature, an "average" is an estimator which, subject to some bias, predicts the value a sequence tends to. My professor was fond of saying, "the function f(x) = 15 is an average, but since it's a constant function it will almost always be a terrible one" to drill this into our minds.

The arithmetic mean is colloquially called the average and differentiated from the median and mode, but technically speaking these are all averages. They are all estimators of central tendency. It would be not be out of the ordinary if a statistician asked, "which average do you mean" for clarity. Which definition of average is best depends on what you're trying to measure.

I dislike this interview question because it's an area where it's 1) more trivia than practical knowledge, and 2) easy to not recognize someone who knows more about it than you do. It's like if I tried to test your knowledge of the difference between "affect" and "effect", and then you correctly used "effect" as a verb and I thought you were wrong.

If I repeated everything I just said about estimators in an interview, the interviewer might think I'm too ivory tower to realize that "of course he's just talking about the mean!" But then I could also ask why I'm being asked a question like this in a software engineering interview.

It's a language game where no one wins (somewhat in the sense of Wittgenstein).