What statistics are susceptible to Simpson’s Paradox? That’s an interesting question you raise, Matthijs Cox. I think you’re mistaken though: the arithmetic mean is definitely among them, just like the median. You can see that illustrated below with my example data:

In this case, the overall mean does move less than the overall median. That could be a general feature of the mean , but I also engineered this case to show an especially big change for the median, so I’m not so sure.

The minimum and maximum would not seem to be affected at all. Some other generalized means do seem to be affected, like the geometric mean. I haven’t checked into root-mean-squared or others.

Worth investigating further!

(I’ve also added the example data to the original post if you’re inclined to check it.)