# Avi Ben-Abraham, man of a thousand and one faces:

July 22, 2001 9:37 PM Subscribe

**unusually high IQs**are seemingly oblivious to the reality that an IQ score becomes effectively unmeasurable at around a z score of 3 to 4, putting lie to their claims of extraordinary IQ (

*not to mention how meaningless an IQ is to begin with...*).

An IQ of 250 is ludicrous in every way. Assuming a standard deviation of 15, as is common in IQ tests (*although some use 16*), 250 would result in a z-score of** 10 **(

*or 9.375 using SD=16*). Converting this into probability/ rarity of occurence requires figuring out the percentile rank for the given z-score. Excel bombs out at z scores of 8, but even a z score of 8 is equal to 15 nines, or 1 in a

**. With estimates that in the whole of human existance about 60 billion people have been born, this means a 1 in quadrillion ranking would mean they were**

*quadrillion**so*smart, the human race would be required to produce more than 16,000 times the number of people it already has in all of our collective existence to create someone like that- and this at an alleged IQ of

*220*. You can, uh, imagine my skepticism about an IQ of "250", probably a few million times rarer still- or that fraud Marilyn vos Savant and her supposed 228 IQ. :)

posted by hincandenza at 3:42 AM on July 23, 2001

Then again, maybe some reverse psychology -- "they'll NEVER think this guy's a spy, he's so obvious!"

posted by delfuego at 8:03 AM on July 23, 2001

posted by delfuego at 8:04 AM on July 23, 2001

*hated*my required statistics & probability course (and I'm a math minor), but I'm beginning to rethink things. Where did you learn the formulae for IQ scores? I really need to see that stuff.

posted by Eamon at 8:46 AM on July 23, 2001

A movie comes to mind. a french spy(?), bufoonish, drunken leaks, it had nick nolte or someone, some flick from the journalist genre. (killing fields, salvador, welcome to sarejevo,deadline,a year of living (very) dangerously etc.) Sun-tzu might categorize him as an expendable.

posted by clavdivs at 9:47 AM on July 23, 2001

posted by clavdivs at 10:03 AM on July 23, 2001

**Eamon:**Search the web for "z score" and "IQ", and I'm sure you'll find plenty of good descriptions of how they are calculated. The basic math is that the test score is normalized to create what's called a Standard Score, which is why we get the "median IQ is 100" and standard deviation is 15 (

*for the Wechsler test; Stanford-Binet and a few others used 16*) for most tests. Standard deviations are useful things; they let us figure out the rarity of a particular score, i.e. the percentile rank, assuming a bell curve distribution. The number of standard deviations from the norm is also known as the z score, so a z score of 1 means IQ=115 (

*1 x 15*), a z score=-2 means IQ=70 (

*-2 x 15*), a z score=2.67 (

*2.67 x 15*) means IQ=140, etc..

A standard normal curve, aka "bell curve", has known percentile ranks for all z scores, and there's a large formula to figure out the exact percentile rank for any z score. The first three to remember are that an IQ of 115 (1 SD above the norm) is a percentile rank of 84.1, IQ=130 (2 SD) is 97.7, and IQ=145 (3 SD) 99.8. So an IQ of 145 makes you- in theory- among the "smartest" 2 out of 1000 people. It's worth noting that these calculations are used for a variety of things; you could easily say that someone's height or weight was a z-score of 2, meaning they were in the top 2.3 % of people based on height or weight.

It's worth noting that generally any scores beyond 3 SDs above or below the norm are called outliers, meaning scores so out of the ordinary that they are discarded as statistically meaningless but worth further investigation (*most IQ tests have a "ceiling" between 160-167*). At 4 SDs you'd have an IQ of 160, or percentile 99.996, but at an IQ of 167, just 7 points higher, is percentile 99.9996,* 10 times *rarer still (

*and a rarity of*). So you can see that beyond a certain point, the significance of a few points becomes so huge, any accuracy or meaning in testing becomes non-existent. My personal feeling is that an IQ of 160 is basically as smart as people get- there doesn't seem to be much difference at that point in how "smart" people are, that they are all about equally smart...

**4 in a million**, a nonsenical proposition since before that level of rarity there'd be little difference in actual intelligenceBy the time you get into the alleged IQs of 180+, you'd be talking about not only a meaningless notion, but a rarity of occurence that changes an* order of magnitude *for every point of IQ. Assuming there ever *was* a "smartest person who ever lived", they'd have had an estimated IQ of 210 *by definition *(*but what, do we quibble over whether Einstein was smarter than Newton? Or Goethe over JS Mill?*). In Excel, you can use the NORMDIST function to figure out exact percentiles- the Excel help file has the exact formula written out- but safe to say it refused to calculate beyond 8 SD, or 1 in a quadrillion; after that, it started rounding to 1, making a score of 228 or 250 a virtual mathematical impossibility in a world population of only 6 billion... :)

posted by hincandenza at 1:31 PM on July 23, 2001

**Thaw**?

posted by topless at 1:14 PM on July 24, 2001

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Great find.

posted by delfuego at 11:25 PM on July 22, 2001