Is this correct? I know no definition where median can be interpreted as an average.

e.g. M-w.com:

> 1 a > : a single value (such as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values

Average isn't well defined-- if you have to guess, people probably intend "arithmetic mean" when they say it. But if you're using it in the sense of a single number that represents the typical value of a dataset, you may want the median, mode, or midrange, or even a geometric or harmonic mean depending upon circumstance.

So it's best to use that term. And it's best to be charitable to not jump on people saying "average" when the median might be the best measure of central tendency for a task.

HN tangent threads are the best.

Hopefully no one nitpicks my use of "tangent" on a digression of an aside...

It's frequently used in when talking about incomes specifically. [0]

> For example, the average personal income is often given as the median—the number below which are 50% of personal incomes and above which are 50% of personal incomes—because the mean would be higher by including personal incomes from a few billionaires. For this reason, it is recommended to avoid using the word "average" when discussing measures of central tendency and specifically specify which type of measure of average is being used.

[0] https://en.wikipedia.org/wiki/Average

The median minimizes the L1 norm and the mean minimizes the L2 norm. (Of the error made between the estimator and the data roughly speaking.)

In this sense yes, median is some kind of average.

But then it is insensitive to the outliners, which is the reason it is suggested above.