# Are there more people with genius IQs living in China than there are people total in the U.S.?

This claim was made popular by being said in the movie The Social Network. It exactly says:

Did you know there are more people with genius IQs living in China than there are people of any kind living in the United States?

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This claim can actually be tested very easily. Others have done it, e.g. Brian Dickerson: The perils of repeating political nonsense and came to the conclusion that the claim was wrong.

You just need the chance a random person from a large group has a genius level IQ, then multiply it with the number of people in China and compare the result with the number of people in the USA. The IQ follows a Gaussian distribution where 100 is the mean by definition and a standard deviation (SD) of 15 (after Wechsler) or 16 (after Stanford-Binet). (sources: [1], [2]). The rarity of a particular IQ can be calculated easily and are listed by [1]. This numbers give the percentage of people with an IQ equal or lower than the given IQ and the rarity of this occurring.

The main question actually is what an genius level IQ is. According to [3] it is 140 or higher ("Genius or near genius") while [4] states it as at least 160. The rarity of such an IQ is 1/261 (with a SD of 15) or 1/161 (SD=16) for an IQ of 140 and 1/31,560 (SD=15) or 1/11,307 (SD=16) for an IQ of 160 [2].

The population of USA for 2012 is about 313,221,000 according to the U.S. Census Bureau [5]. The population of China for 2011 is about 1,370,537,000 [6]. Taking the lowest rarity of 1/161 from above then there are about 1,370,537,000/161 = about 8,513,000 geniuses in China, which is significant less then the 313,221,000 Americans. If you take the 15 SD value of 1/261 then you get only about 5,251,000 Chinese geniuses. With the 160 IQ points, which are more realistic [7] to indicate a real genius, the numbers are even much less (about 43,400 or 12,100). Note that 1,370,537,000/313,221,000 = 4.375, so in order for this claim to be true actually one of every four (or say five) Chinese would need to be a Genius. Even without the numbers above, it can be easily understood that this is not the case.

Conclusion: This claim is wrong according to the definition and probabilities of the IQ.

### Supplement:

It has been pointed out, that there are published research results [7] showing that China and other Asian countries have an higher average IQ of about 106 (or even as high as 115) as the normed average of 100. This would increase the number of geniuses in China: The above factor of 1/161 would drop to about 1/60 or, for an Chinese average of 115 even to about 1/17. These numbers can be easily calculated using the standard deviation, e.g. using MS Excels function `NORM.DIST(140, 106, 16, TRUE)`. However, both these factors are not in any way close to the US/Chinese population ratio of about 1/4.375, so the original conlusion still holds.

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Doesn't this assume a proportional distribution of IQ between the 2 countries? I know it would take a lot to skew the numbers that much, but it does leave the numbers dubious? – Marc Gravell Mar 21 '12 at 19:01
@MarcGravell: Yes, it assumes that. Actual IQs might differ due to health, nutrition, education and other living conditions. Also you can assume that many of these are better on average in the USA than in China, so it counts against the claim. Your (now edited away) worldwide idea is good: 7,002,000,000 (World wide) / 313,221,000 (USA) = 22.35, so as long not every 22nd person in the world is a genius this claim can't be correct. While this is higher than the 4.375 before it is still out of the question that so many people on earth are geniuses. – Martin Scharrer Mar 21 '12 at 19:16
@MarcGravell: Even if the numbers are not very exact (especially given the missing exact definition of "genius") the last part says it all: Every forth Chinese would have to be a genius in order for this claim to be true. You don't need to do any actual math or research to understand that this can't be the case. – Martin Scharrer Mar 21 '12 at 19:20
Not that this would invalidate your calculation, but the way it is written, it seems like you're saying that a genious IQ is 15 or 16 standard deviations above the mean, and not that the considered SD is of 15 or 16... – tpianca Jan 5 '14 at 1:19
@tpianca: Ok, I see what you mean. I rephrased it now. Thanks! – Martin Scharrer Jan 5 '14 at 9:50

## protected by Oddthinking♦Jan 5 '14 at 2:02

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