[Jtsummers]

That's how it's often used. People might say something like, "half the people are below average". But if you ask the same person: What's the average of [4,5,9,10,10]? They'd answer 7.6 (after doing the math). This dual meaning creates confusion, and its why, at least those reporting on things, should clarify whether they mean the mean or the median. Similarly, as the old adage goes, there are lies, damn lies, and statistics. People will take advantage of the misperception of "average" and report a mean as "the average", even though it hides the truth. For instance, around here people refer to the "average" income, some number like 50-60k, when the median income is actually around 40k. Or the average government employee salary, when again the median works out to be lower than the mean, which is what they report(here, won't claim mean is always greater than median as it can obviously be skewed either way).

[mcv]

I think a lot of people blindly assume a standard distribution (where medium and average are the same) because that's very often correct.

[Jtsummers]

That doesn't absolve those responsible for reporting figures (or misreporting figures) of the responsibility of clarity. Mean and median are often quite distinct, especially in economic and financial figures, and reporting one as the other because it makes the point they're going for is disingenuous.

Another instance of statistics reporting abuse: doing <something> will increase your risk of <something> by <some percent>. It totally ignores that the original odds were so far against it ever happening that that increase may be double the risk or even 5 times, but it's still 1 in a million odds. Since the typical person has little more than a high school level of mathematics, and probably not a statistical course in that, they're easily thrown off by this sort of reporting.