You're quite probably right about common parlance..
> but it's not the correct technical language.
..but as you point out it's not really appropriate in a technical context, indeed I don't think I've come across the term "average" being used in this way in technical literature; I've normally either seen expectation (for probability theoretic cases) or mean (for statistical cases).
> So nobody should be hard on themselves for not knowing the difference.
Absolutely, which is why I think being hard on someone for not knowing the difference between "the average" and the median is similarly an issue.
Incidentally, "mean" doesn't quite cut it, if you want to be a stickler about it. There are several types of means: arithmetic, geometric, harmonic, etc. By that standard, you just failed the interview.
I'm going to assume, then, that you didn't read my original comment which started off this line of discussion? By that standard, you just failed the interview. ;)
Although I do know that "average" covers mean, median and mode, when I was young I was not taught that way. First I was just taught "average" with a formula, and many years later "median" and "mode". I don't think I noticed the term "mean" until I learned about median and mode.
You can see this reflected in scientific calculators used at school, where the button for calculating mean is labelled "Avg".
And in Microsoft Excel or LibreOffice Calc, the function to calculate mean is called "AVERAGE".
So nobody should be hard on themselves for not knowing the difference. You probably weren't taught the difference, and common tools work against it.
It looks to me that the common word for statistical mean is "average" in English, but it's not the correct technical language.