The word average is often used to mean mean, however it can be used less specifically - median is a type of average as well.
From Merriam-Webster definition of average:
1a) a single value (such as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values
Also, things like testosterone levels in a population usually follow a normal distribution, where both mean and median are the same, so the distinction is often meaningless for practical purposes
Not true, I am a naturalized US citizen, and don’t have a middle name - it was never an issue and I was never asked to come up with one. My son was born in the US and also doesn’t have a middle name.