According to a recent meta-analysis, the correlation between IQ and school grades in the general population is nearly 0.55. Meanwhile the correlation between IQ and years of education in the U.S. is also 0.55. Given the similarity between these two correlations, we can think of them both as just the 0.55 correlation between IQ and academic success.
So in a typical elementary school class (where you have the full range of cognitive ability, including dull students who will drop out later), 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 academic success “only” correlates 0.55, the best and worst students in the class should have IQs only 55% as extreme: 85 and 115 respectively (U.S. norms).
Of course, elementary school grades are only one way we can quantify academic success in the general population. Another way, as mentioned above, is years of schooling or highest degree obtained.
High school dropouts: IQ 85 (U.S. white norms)
In 2006, roughly 17% of American adults, aged 25+ lacked a high school diploma or equivalent. That means that the median high school dropout was in the bottom 8.5% of education. If you’re in the bottom 8.5% of IQ, you’d have an IQ of 80 (U.S. norms), or 20 points below the U.S. mean of 100. But since the correlation between IQ and education is only 0.55, we’d expect high school dropouts to be only 55% as far below the mean, thus have an average IQ of 0.55 (-20) + 100 = 89 (U.S. norms)
According to a source provided to me by commenter C, the actual average IQ of Americans with only a 9th to 11th grade education (age 20-90) tested in the WAIS-IV 2006 norming was just as expected: 88.77 (U.S. norms); 85 (U.S. white norms)
University grads: IQ 108 (U.S. white norms)
By 2006, roughly 26% of American adults, aged 25+ had a bachelor’s degree or more. That means that the median university graduate, is in the top 13% of education. If you’re in the top 13% of IQ, you’d have an IQ of 117 (U.S. norms), in other words, 17 points above the U.S. mean of 100. But since the correlation between IQ and education is only 0.55, the expected IQ of university grads would be 0.55(17) + 100 = 109 (U.S. norms).
How close does this prediction come to the actual data? The actual IQ of U.S. university grads (age 20-90) tested in the WAIS-IV 2006 norming was 110.77 (U.S. norms); 108 (U.S. white norms).
PhDs: IQ 119 (U.S. white norms)
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” 0.55, each point above 100 must be multiplied by 0.55, reducing the expected average IQ of PhDs to about 121(U.S. norms); 119 (U.S. white norms).
The only actual recent data on the IQs of U.S. PhDs that I’m aware of comes from Charles Murray’s book Coming Apart, which reported that for PhDs turning 25-29 in 2005-2009, the average IQ is 124 (U.S. norms). However this is probably too high because (1) Murray’s sample was limited to white PhDs, and (2) the test used was the AFQT, which is arguably an achievement test, not a conventional IQ test, and thus might over-correlate with education. The true average IQ of PhDs is probably several points lower, just as simple regression would predict.
Harvard students: IQ 125 (U.S. white norms)
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 0.55, the median Harvard student should be only 55% as far above 100. Thus, simple regression predicts the typical Harvard student should have an IQ of 129 (U.S. norms).
Actually a sample of Harvard students studied by Harvard psychologist Shelley Carson and her colleagues clocked in at IQ 122 (U.S. norms); 120 (U.S. white norms) on an abbreviated version of the Wechsler intelligence scale. On the other hand, Harvard undergrads are rumoured to average 166 on the LSAT, which equates to an IQ of about 132 (U.S. norms). The abbreviated Wechsler estimate is perhaps too low because of ceiling bumping, poor sampling, and an over-emphasis on spatial ability, but the LSAT score may be too high because it’s too much of an achievement test. Averaging them both gives an IQ of 127 (U.S. norms); 125 (U.S. white norms). Very similar to the predicted level.
I completely ignored the stratospheric SAT scores of Harvard undergrads because being selected by this test, it’s an outlier on which they score high by definition.
Tenured professors: IQ 127 (U.S. white norms)
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 0.55, we should expect the average tenured professor to be around 128 (U.S. norms); 127 (U.S. white norms) 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.
Academic Nobel Prize winners: IQ 148 (U.S. white norms)
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 IQs 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 0.55, the average Nobel laureate should have an IQ of 141 (U.S. norms); 140 (U.S. white norms).
The only data on the actual IQs of Nobel level scientists is probably outdated. In the Roe study, the average IQ of eminent scientists was 166 on a verbal test (the best proxy for IQ in the study). On the other hand, in the Terman gifted study, the IQ of the two kids who would grow up to win a Nobel Prize was 129 (too low for the study). The Roe study average was probably too high because of the academic nature of the test, and because the sloppy way the test was normed, while the Terman study suffered from too small a sample of Nobel Prize winners perhaps tested at too young an age. Averaging both studies together gives IQ 148 as the best estimate for academic Nobel Prize winners. This is higher than predicted by simple regression from IQ and academic success, perhaps because the data is outdated, or perhaps because at the highest levels, academic achievement becomes more creative, thus increasing the correlation.