Medians, averages, and the peak of a probability distribution are all distinct in the general case.

You can't be stupider than a rock, but there seems to be no upper definite upper limit to human intelligence.

Hence the IQ curve isn't a Gaussian. It isn't symmetric. The average is dragged upwards by very-high-IQ people, above the median.

This is like a billionaire moving to some tiny country town. The average income suddenly becomes much higher, but the typical (median) income doesn't budge.

Rich people is a useful analogy to the point I'm trying to make.

When I was on holidays in Vietnam, my chauffeur was horrified to hear that I was too tired and that I wanted to skip a pre-paid dinner reservation at a "fancy" restaurant and that I preferred to simply go to my hotel and crash. That fancy dinner was something like $20. To him that's a lot of money. To me it's nothing. Meanwhile I hear about rich Saudis abandoning italian supercars because they're "broken" in the same way my kid throws away broken toys.

Intelligence and wealth are vaguely similar. People used to a certain level just can't wrap their heads around how people at different levels do things.

> but there seems to be no upper definite upper limit to human intelligence

I assure you this does not seem to be the case.

There is an observed, and inexact, upper limit on human intelligence, just as there is with human height, and for broadly similar reasons: gravity, in the case of height, and for intelligence some much more hand-wavey limit to the amount of neurons and dendritic links a human body can construct inside a skull which has to fit through hips which are capable of bipedal motion.

(Some of you are curious, and yes, there is a real correlation between skull volume and measured intelligence, but let's not bust out the calipers because it's a bad proxy for something we can measure more accurately with tests).

Hence the IQ curve is, in fact, Gaussian, just as human height is, despite the fact that you can't be shorter than a mushroom, and the Empire State Building is an existence proof of very tall things.

>> You can't be stupider than a rock, but there seems to be no upper definite upper limit to human intelligence.

But to conclude from this that most are below average, wouldn't you have to know that the high IQs pull the average up more than the low IQs pull it down? I don't see how the mere assumption that there's no upper limit gets you there (not to mention that this assumption is bound to be wrong anyway). But as you say, maybe there's a reason I'm in the big half...

The analogy to power-law distributed wealth where some people clearly tangibly do have a billion times more than other people feels stretchy. To the extent that standardised IQ tests adequately quantify intelligence, Marilyn vos Savant might have busted out of the constructed Gaussian distribution by registering 2.28x the average score, but she's comfortably outnumbered by people lacking the ability to register a score in cognitive ability tests. And if anything, the score range probably inflates the differences in overall capability given the respective quantifiable intellectual achievements of people on the upper side of the bell curve seem to be more about specialism and motivation than dozens of point differences in test scores...