In the book, A Question of Intelligence by Daniel Seligman, he reports (pg xiv) that the correlation between IQ and elementary school grades is 0.65. This correlation is far from perfect since how hard you work is just as important to grades as how smart you are, but the correlation is still very high (as high as many IQ tests correlate with each other). The correlation drops in high school and drops further in university, but that’s probably because as you move up the educational ladder, a lot of low IQ people drop out, so there’s less IQ variation for grades to correlate with. But in elementary school, you have virtually the full range of cognitive ability, so it’s a good place to understand the true relationship.
So in a typical elementary school class, you might have 30 students, which means that the lowest IQ in the class should be 28 points below average and the brightest in the class should be 28 points above average (IQ 72 and 128 respectively). However because IQ and grades “only” correlates 0.65, the best and worst students in the class should have IQ’s only 65% as extreme: 82 and 118 respectively.
Of course, elementary school grades are only one way we can quantify academic success in the general population. Another way is years of schooling or highest degree obtained. In the U.S., a PhD roughly marks the top 1% in years of completed education, which suggests that the median PhD is in the top 0.5% in education level. If there were a perfect correlation between IQ and academic success, we’d expect the average PhD to have an IQ of 138 (the top 0.5%), but since the correlation is “only” 0.65, each point above 100 must be multiplied by 0.65, reducing the average PhD to their actual IQ which is around 125 (still very high!).
IQ’s of Harvard students
Are there academic achievements more impressive than getting a PhD? Yes. Getting acceptance into Harvard: the world’s most prestigious university. Out of the 4.1 million 18-year-olds in the U.S. in a given year, only about 1600 go to Harvard. So if there were a perfect correlation between IQ and academic success, the dumbest Harvard student would have an IQ of 150 and the median might have an IQ of 153. However because the correlation is only 0.65, the median Harvard student should be only 65% as far above 100. Thus, simple regression predicts the typical Harvard student should have an IQ of 134. Actually a sample of Harvard students studied by Harvard psychologist Shelley Carson and her colleagues scored somewhat lower on an abbreviated version of the Wechsler intelligence scale:
Eighty-six Harvard undergraduates (33 men, 53 women), with a mean age of 20.7 years (SD = 3.3) participated in the study. All were recruited from sign-up sheets posted on campus…The mean IQ of the sample was 128.1 points (SD = 10.3), with a range of 97 to 148 points
On the other hand, the average Harvard student has an post-1995 SAT score (reading + math) of 1490, which according to my formula equates to an IQ of 141.
The SAT likely overestimates Harvard intelligence because when you select people who did especially well on one test, you are also selecting people who got lucky, were well prepared and overperformed on that one test. Such people will likely regress to the mean when given a test that wasn’t used to select them. On the other hand the abbreviated WAIS may have underestimated Harvard students because it’s a very brief test, and thus gives only rough results. Averaging their scores on both tests, gives an IQ of about 135. Almost identical to what simple regression predicted based on the 0.65 correlation between IQ and academic success.
IQ’s of tenured professors
Another form of academic accomplishment that’s about as exclusive as attending Harvard is becoming a tenured university professor. Scientist Steve Hsu wrote:
…when an attorney prepares a case it is for her client. When a Google engineer develops a new algorithm, it is for Google — for money. Fewer than one in a thousand individuals in our society has the privilege, the freedom, to pursue their own ideas and creations. The vast majority of such people are at research universities. A smaller number are at think tanks or national labs, but most are professors…
So in terms of academic success, being a full tenured professor is a one in thousand level accomplishment. If there were a perfect correlation between IQ and academic success, the dumbest tenured professor would have an IQ of 147, and the average tenured professor would probably be around 150. But since the correlation is 0.65, we should expect the average tenured professor to be around 133 with quite a bit of variability around that mean, depending partly on the prestige of the university they teach at and the g loading of the subjects they teach.
IQ’s of Nobel Prize winners
Are there academic accomplishments more impressive than becoming a professor or going to Harvard? Yes: Winning the Nobel Prize. Many years ago a respected psychometric expert named Garth Zietsman wrote an article about using this type of regression to estimate the IQ’s of Nobel laureates, though I don’t remember the exact stats he used.
But let’s say only one in a million American adults has a Nobel prize (excluding the Nobel peace prize which is non-academic). If there were a perfect correlation between IQ and academic success, we’d expect the dumbest American Nobel laureate to have an IQ of 171 and the average Nobel laureate to be around 174. But again, since the correlation is 0.65, the average Nobel laureate should have an IQ of 148, or roughly 150 if you like nice round numbers. Of course there would be a lot of variability around the mean. Those who earned their Nobel prize in hardcore intellectual subjects like physics would likely average above 150. Those who earned their prize in more subjective and artistic subjects like literature would likely average well below 150; indeed probably below 140.
Is it plausible that the average academic Nobel prize winner has an IQ around 150? Yes: In the early 1950s, Harvard psychologist Anne Roe intelligence tested extremely eminent scientists who were very close to Nobel Prize level. She found they had an average Verbal IQ of 166, an average Spatial IQ of 137, and an average Math IQ of 154. These are very inconsistent results suggesting there might have been problems with how the tests were created and normed. Nonetheless, if you average the three scores to cancel out the error, you get an IQ of about 150.