```
Actually all this tells us is that she's good at doing IQ tests https://t.co/jg0EQIT8ht
— Sam Bowman (@s8mb) January 8, 2016
```

Meet the kid with an IQ higher than Einstein. And another one, and another one, and this one, and this one, and this one, and these ones.

Let's ignore the elephant in this room for now. |

What's going on here with all these identical articles?

Firstly, IQ tests are valid, mainstream psychology, and anyone who takes Sam's joke seriously is completely ignorant of the literature. For more, my friend Stuart's book is a good introduction.

Secondly, we don't know what Stephen Hawking's or Albert Einstein's IQs were, since they never sat a full IQ test in controlled conditions. The estimations of their IQs are complete speculation, and should be ignored.

That said, these kids are getting very high scores. On commonly used IQ tests, results are standardised to a normal distribution, with a mean of 100 and a standard deviation of 15.

With thanks to the website 'mathsisfun.com'. |

This means 34% of the population will have an IQ within one standard deviation above the mean (100-115), and another 34% one standard deviation below it (85-100). 162 is 4.1 standard deviations above the mean (z=4.1). Unfortunately mathsisfun.com can't cope with a child this smart, they're simply off the chart. But using a different normal distribution calculator, I came up with a percentage of 0.0021. That is, one in 48000. We live in a big country, so there will be plenty of people that smart, probably around 1300 in the UK.

I guess it's plausible there would be quite a few kids this smart, but most kids will never take an IQ test, even really smart ones, and why are they all 12 year old girls? And how did a single school have 56 of them?

The answer is that mensa don't use the more common IQ tests. They use one called the Cattell III. This test still has an average of 100, but the standard deviation is 24, quite a bit higher. This flattens the curve, the best will get higher scores, the worse will get lower (but are unlikely to take the mensa test anyway). The consequence of this is that a maximum score of 162 is much less impressive. It is 2.6 standard deviations above the mean, and so we would expect 0.47% of the population to get this maximum score. Translating this into the regular, st dev 15 scale, gives us a much lower score of 139.

That is, in a random sample of about 200 people, you'd expect someone to get this maximum score. It really isn't that impressive. Mensa accept the top 2% of the population, so for a large school to have 56 kids in that bracket is hardly surprising.

I guess it's far too much to ask that newspapers stop writing these identikit stories, but even most people even who know a bit about IQ testing aren't aware that the standard deviations are different, and that therefore the scores aren't immediately comparable. I don't want to say that their system is vanity scoring, it's administered in controlled conditions, and is much better than any online IQ test, but also it's basically vanity scoring.