Earlier quoted context omitted.
Calling all the measures of central tendency "averages" is colloquial, not formal. Check your sources if you're going to nitpick my nitpicking. Saying "literally" in place of "figuratively" and then referencing the Oxford dictionary (meaning C, look no further) is a cool way to troll, and to make a fool of oneself.
I don't understand why you're mad that someone cited the Oxford definition to you. It's not trolling. You're wrong, and you can see this by looking at any number of published news articles where more often than not, average is used to mean median. You can see this from the way that we use average to mean typical. 'Typical' features are more likely to be median or mode than arithmetic mean. 'Average' is itself a collo…
¹ This makes "average" a particularly weird "false friend" vocable, because the average recipient might well take it to mean what you think it means, but might also understand it as a very closely related, but subtly different thing.