12-Year-Old Headed to Cornell University as a Student

Yes, but a person’s height has a precise definition that involves using an engraved platinum meter stick shipped direct from the NIST plus some painful medieval torture device to hold their spine straight. The population distribution is whatever it is … approximately normal but not truly so.

Similarly, once we are given a set of prices, stock returns also have an exact definition as (final price / initial price - 1). Their distribution is whatever it is … as you point out, it is kurtotic, heteroskedastic, etc.

There has to be a precise (cardinal) definition of IQ in order to even have the statement “IQ isn’t distributed normally” not be meaningless.