"IQ is merely a statistical bell curve with the score being a placement of a person on this curve with the average set to 100 and half the population on either side. In a normal IQ test, the standard deviation is set to 15, and following the rules of a normal curve, it follows about 64% of the population will fall into the 85-115 range that we designate as "average." 18% will be below that range, while 18% will fall into the above average category at 116+.
An IQ of 145, which is 3 standard deviations above the mean corresponds to about the top 0.145% of the population, or 1/741. It's an exceptionally rarefied category to fall into and drops off rather precipitously to the point that only 5 points of gain to 150 means only about 0.04% of the population are at that point or higher, a tiny 1/2330.
By 160, 4 standard deviations above the mean, only 0.004% remain unaccounted for on lower IQs. Only 1/31,560 have an IQ of this level or higher. 5 standard deviations, or 175 and up are found in only 1/3,483,046 people. In all of the United States, there are statistically less than 100 people with an IQ of 175 or more.
Finally, 6 standard deviations, an IQ of 190 is quite literally encountered in statistical terms in one out of every billion people. There are quite possibly no more than 6 or 7 on the entire planet if the statistics hold up at this level.
At 201, which is the highest meaningful number, 99.9999999995% of all people are accounted for at this score or a lower one. Theoretically, a higher score could be found as the statistical function is asymptotic and will never reach zero, but IQs of 201 or higher are found in only 190 billion people in statistical terms, meaning perhaps ONE has existed in all of human history, if that!
Yes, you could get a score of 300... but in statistical terms, it would set a person apart probably to the point of being one out of some incredibly high number expressable only in scientific notation. It would be 13.33 standard deviations above the norm.
It is theoretically possible to have an IQ of 300 as it's not mathematically impossible given the way the IQ curve works.
However, such a person would probably be about 1/(1x10^23) or more in rarity, quite possibly more. On a statistical level, he would be completely unexpected given the fact that such a rarity would far outpace the number of humans who are alive or have ever lived, or indeed, probably will live in the next 10000 years. It's a bit like getting hit by lightning while your plane is crashing shortly after you won the lottery in terms of probability..." - random Internet user