When people say "better than average", their intuition tends to be "better than half" (the concept here is the median), as opposed to "better than a particular

When people say "better than average", their intuition tends to be "better than half" (the concept here is the median), as opposed to "better than a particular number that happens to be the average value of that hing" (the concept here is the average or arithmetic mean). And in this context indeed only 50% can be above median. People's intuition of stats is not that bad actually, but most invariably fuck up when it comes to mapping their fuzzy intuitive concepts to mathematical concepts: they make the mistake of mapping their "intuitive average" with the "mathematical average" when instead it should map to the "median". And yes, for people that understand the word "average" as "arithmetic mean" (as Excel does and most technically literate people do), there is no such "intuitive average" and its wrong mapping to math. But for "lesser minded" people it works like described above, and in their understanding of the words (incorrect... but real, as this how their minds work), the phrase "but only 50% of people can be above average!" is actually valid.