Median is an average.

There are three generally used measures of central tendency:

- The mean: the "arithmetic average", sum of observations divided by count.

- The median: the central measure. The single value (or averaged pair) at the center point of an ordered listing.

- The mode: the most frequently occurring measure. Sort a set of values by frequency, and pick the most frequent instance.

Most people intend "mean" as "average", but that's not strictly the case.

https://en.wikipedia.org/wiki/Average

For our next pedant's corner post, we'll take on the distinction between descriptivist and prescriptivist definitions.

I have never, ever heard anyone colloquially use the word 'average' and mean anything except 'mean'.

I have heard it all the time for median. Average height, average wealth, ect.

But people usually are expecting mean in your two examples.

I think they mean the median. Median income in a group of people is usually smaller than the mean becomes of extremely wealthy outliers.

If someone says something about the "average person", they are not talking about the mean, they are talking about the median.

It's possible that median is a better measure of central tendency for those things. It also sounds like you're interpreting their use of 'average' as meaning median when you think that would make more sense, rather than asking them (and in fairness, I don't usually grill people on which measure they're thinking of when they say 'average' either). In my experience, people who actually understand the different measures of central tendency usually (on average, heheh) specify one explicitly. The rest of the population is probably only aware of arithmetic mean.

Intelligence is approximately a normal distribution so the mean and median are almost exactly the same.

Ha! It is, but “median” just doesn’t pack the same snarky punch.