The key piece of the puzzle is IQ is a scale that is specifically manufactured to be normed around a mean of 100 (with median usually close to 100) while also exhibiting bell-shaped form up to a couple of standard deviations either side of the mean.
Crucially this involves monotonic but non-linear rescaling of test score distributions that are often already asymmetric or fat-tailed (this is what
@ThePrimeagen is alluding to here). Scores are non-linearly warped to create roughly symmetrical mass about the mean while preserving rank. This geometry is by design, not a discovery!
Therefore everything we’re tempted to infer from IQ models at the tails (±3 SDs and beyond) becomes increasingly unreliable, and left and right tails are differentially unreliable due to non-linearity and floor/ceiling effects.
Yet, entire careers have been made splashing around in these tails like they are truth preserving. The lesson is to not take everything in the IQ literature totally seriously, while also respecting its predictive power up to roughly ±2-3 SDs from 100.
I welcome
@nntaleb to utterly eviscerate me if I got anything wrong here.
i love how people say "half the people are dumber than the average iq"
lil bro its the median ya goof, the average is skewed by outliers
looks like we found someone below the half way point