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> I discovered Georgios had an IQ of 145, a score in the top 1.33% for the test he took. Put simply, that meant that he was several “mental years” ahead of his

> I discovered Georgios had an IQ of 145, a score in the top 1.33% for the test he took. Put simply, that meant that he was several “mental years” ahead of his peers. If a teacher taught fifty students a year for forty years, they would only meet two or three children with his raw ability. Unless I'm mistaken, this appears to be off by an order of magnitude.

kazinator 3y ago
Not to mention that such an IQ is not simply several "mental years" ahead of people who are at 100, it's a qualitative difference to which the 100 cannot catch up.
riwsky 3y ago
It is. The percentage is wrong; the “only two or three every forty years” is right (by construction, IQ has a mean of 100 and stddev of 15).
pdonis 3y ago
AFAIK 145 IQ is three standard deviations above the mean in a normal distribution, and only 0.3% will have that score or higher, so I think the article is off by a factor of about 4.
- gnicholas 3y ago
  Looks like the 1.3 percent was the part that was off. It’s .13 percent: https://www.davidsonacademy.unr.edu/blog/what-does-profoundly-gifted-mean/#:~:text=What%20IQ%20is%20Considered%20Profoundly%20Gifted%3F,and%20are%20considered%20profoundly%20gifted https://www.davidsonacademy.unr.edu/blog/what-does-profoundl.... So the end result is accurate, it would be 2-3 students with that ability level.
- HALtheWise 3y ago
  Nitpick: 0.3% will be outside three standard deviations to either side, with 0.13% above and 0.13% below.
  - pdonis 3y ago
    Ah, yes, you're right, we're only interested in the upper tail.
tzs 3y ago
On the usual IQ scale 145 is 99.865 percentile. In 2000 (50 per year x 40 years) you would expect 2.7 with that IQ or higher, so that part seems right. I think what is going on is that when it says "top 1.33% for the test he took" it is referring to some test given to children who are already known or expected to have high IQs, and on that test people with IQs of 145 are 98.67 percentile.
- gnicholas 3y ago
  I agree with the first part but question the second. It appears that the author was off by precisely one order of magnitude, having mixed up .13% and 1.3%. It could be chance, but I think it’s probably a simple mathematical error. The author's conclusion (2-3 children over a career) is correct, but the intermediate step is mistaken.
  - nativeit 3y ago
    Even if it’s .13%, that is by definition “in the top 1.3%”. Pedantry—the warm refuge of everyone else in the 99.87%!
HALtheWise 3y ago
Using the standard definition of IQ (mean 100, std dev 15), 145 is +3 standard deviations, so that should be in the top 0.135%, which is consistent with the 2-3 students per career number. I'm not sure where the article got the 1.3% number, it could be either a decimal point error, or this could be a specific test that's primarily given to gifted students and so both numbers could be correct.

kazinator 3y ago

Not to mention that such an IQ is not simply several "mental years" ahead of people who are at 100, it's a qualitative difference to which the 100 cannot catch up.

riwsky 3y ago

It is. The percentage is wrong; the “only two or three every forty years” is right (by construction, IQ has a mean of 100 and stddev of 15).

pdonis 3y ago

AFAIK 145 IQ is three standard deviations above the mean in a normal distribution, and only 0.3% will have that score or higher, so I think the article is off by a factor of about 4.

gnicholas 3y ago
Looks like the 1.3 percent was the part that was off. It’s .13 percent: https://www.davidsonacademy.unr.edu/blog/what-does-profoundly-gifted-mean/#:~:text=What%20IQ%20is%20Considered%20Profoundly%20Gifted%3F,and%20are%20considered%20profoundly%20gifted https://www.davidsonacademy.unr.edu/blog/what-does-profoundl.... So the end result is accurate, it would be 2-3 students with that ability level.
HALtheWise 3y ago
Nitpick: 0.3% will be outside three standard deviations to either side, with 0.13% above and 0.13% below.
- pdonis 3y ago
  Ah, yes, you're right, we're only interested in the upper tail.

tzs 3y ago

On the usual IQ scale 145 is 99.865 percentile. In 2000 (50 per year x 40 years) you would expect 2.7 with that IQ or higher, so that part seems right. I think what is going on is that when it says "top 1.33% for the test he took" it is referring to some test given to children who are already known or expected to have high IQs, and on that test people with IQs of 145 are 98.67 percentile.

gnicholas 3y ago
I agree with the first part but question the second. It appears that the author was off by precisely one order of magnitude, having mixed up .13% and 1.3%. It could be chance, but I think it’s probably a simple mathematical error. The author's conclusion (2-3 children over a career) is correct, but the intermediate step is mistaken.
- nativeit 3y ago
  Even if it’s .13%, that is by definition “in the top 1.3%”. Pedantry—the warm refuge of everyone else in the 99.87%!

HALtheWise 3y ago

Using the standard definition of IQ (mean 100, std dev 15), 145 is +3 standard deviations, so that should be in the top 0.135%, which is consistent with the 2-3 students per career number. I'm not sure where the article got the 1.3% number, it could be either a decimal point error, or this could be a specific test that's primarily given to gifted students and so both numbers could be correct.