Commenter Deeru asked me to convert GMAT scores to IQ equivalents. This is always tricky because while IQ tests are normed on the general population of Western countries, college admission tests are normed on only the educated segment of a population, so converting from one type of norming to another requires some assumptions.

According to Wikipedia:

The

Graduate Management Admission Test(GMAT(/ˈdʒiːmæt/ ())) is a computer adaptive test (CAT) intended to assess certain analytical, writing, quantitative, verbal, and reading skills in written English for use in admission to a graduate management program, such as an MBA.JEE-mat^{[3]}It requires knowledge of certain grammar and knowledge of certain algebra, geometry, and arithmetic. The GMAT does not measure business knowledge or skill, nor does it measure intelligence.^{[4]}According to the test owning company, the Graduate Management Admission Council (GMAC), the GMAT assesses analytical writing and problem-solving abilities, while also addressing data sufficiency, logic, and critical reasoning skills that it believes to be vital to real-world business and management success.^{[5]}It can be taken up to five times a year. Each attempt must be at least 16 days apart.^{[6]}

It’s ironic how they deny the GMAT is an intelligence test, while in the next sentence describing it is a test of “problem-solving abilities” because one of the most common definitions of intelligence is the (cognitive) ability to problem solve. It’s clear that the people who make the GMAT are trying to have their cake and eat it too. They want the predictive validity of an IQ type test, while at the same time, want to be seen as good liberals who don’t believe in IQ.

Of course any test that measures literacy and numeracy will tend to correlate substantially with *g* (the general factor of all cognition, measured by IQ tests) whether the test manufacturers intended it to be an IQ test or not because symbolism itself (words and numbers) is a defining feature of the human intellect.

Here’s some basic GMAT data:

My first observation is that from about 300 to 700, GMAT scores are more or less normally distributed with a mean of 551.94 and a standard deviation (SD) of 120.88.

**GMAT scores of 300 to 700**

If we assume that the GMAT population is roughly equivalent to the U.S. college graduate population (mean IQ 111, SD = 13.5), compared to the general U.S. population (mean IQ 100, SD = 15), then the following formula equates GMAT scores to IQ equivalents (U.S. norms):

Formula one (for GMAT scores of 300 to 700):

IQ = [(GMAT score – 551.94)/120.88](13.5) + 111

**GMAT scores of 700 to 800**

However much like the pre-1995 SAT, GMAT scores seem to become much more rare than the Gaussian curve would predict at the highest levels (perhaps because of ceiling bumping or even Spearman’s Law of Diminishing Returns reducing the correlation between sub-sections). For example, a score of 800 is 2.05 SD above the GMAT mean, which on a Gaussian curve, predicts one in 52 GMAT testees should score 800. Instead Deeru claims only one in 6,667 scores this high!

But in order to map this to the IQ scale, we need to know how many people would score 800 on the GMAT if all four million 22-year-old Americans took the GMAT every year (including college dropouts, high school dropouts etc).

I begin with the assumption that the higher you would score on a graduate school admission test, the more likely you are to actually take such a test (given the correlation between academic talent and education level). and so roughly 100% of U.S. 22-year-olds who would score perfect on a graduate school admission test, actually take such a test, and whatever shortfall there may be is roughly balanced by perfect scoring foreign-test takers, or test-takers from other age groups.

Thus people who score perfect on graduate school admission tests did not merely score higher than those who are applying to graduate school, but they scored higher than all 22-year-olds in America, if all 22-year-olds took these tests.

So if only 30 people a year score perfect on the GMAT, does that mean that only 30 of the four million 22-year-olds in America each year would score 800 on the GMAT? No, because there are many genius 22-year-olds who would have scored 800 on the GMAT had they decided to major in business, but instead are busy acing the LSAT or the GRE or the MCAT etc.

Only 23.6% of advanced degrees are in business, thus I estimate that only 23.6% of people who write graduate school admission tests are writing the GMAT. But if 100% of aspiring grad students wrote it, then the number scoring perfect each year should jump from 30 to 127.

So assuming roughly 100% of U.S. 22-year-olds who would have scored perfect on grad school admission tests actually take said tests (and whatever shortfall is roughly balanced by foreigners and other age groups), and assuming only 23.6% of said testees take the GMAT in particular, then:

**if all four million U.S. 22-year-olds took the GMAT, only 127 would score 800, which means that an 800 is a one in 31,497 level score. This equates to an IQ of 160 (U.S. norms).**

So given that:

GMAT 800 = IQ 160

and given that 700 = IQ 128 (per formula one), then the following formula equates high GMAT scores to IQ (U.S. norms):

formula two (for GMAT scores 700 to 800):

IQ = 0.32(GMAT score) – 96

I do not consider the GMAT or any other college admission test to be a particularly good measure of intelligence, however when scores from actual IQ tests are not known, the above conversions are a useful proxy.

**THEY SHOULD NOT HOWEVER BE USED TO ESTIMATE THE MEDIAN IQ OF ELITE BUSINESS SCHOOLS BECAUSE SUCH STUDENTS ARE SELECTED BASED ON GMAT SCORES WHICH MEANS GMAT PERFORMANCE IS NOT A RANDOM SAMPLE OF ELITE BUSINESS SCHOOL INTELLIGENCE. THIS SUBTLE CONCEPT HAS PROVEN EXTREMELY HARD FOR MANY READERS, BLOGGERS AND SCHOLARS TO GRASP! YOU’RE EITHER HAVE A STATISTICALLY INTUITIVE BRAIN OR YOU DON’T. IT’S GENETIC!**

Clifford S Barney

said:It’s been awhile since I took it – 1995. I took it by myself at a noisy military air base with constant interruptions (air base operations center was the only place they could proctor me officially). Very challenging test-taking environment, but I scored a 760.

Eduardo

said:Mensa accepts GMAT scores from percentile 95%. A GMAT score of 730 corresponds to 96% and 720 to 94%. However, from your formula we have an IQ of 137 sd 15 for a GMAT score of 730 and 134 sd 15 for 720.

Also, Triple Nine Society accepts a GMAT score of 746 or above, which by your fomula would be an IQ of 142 sd 15.

We all know that Mensa is 98% which means an IQ of 130 sd 15 and Triple Nine is 99.9% which means an IQ of 146 sd 15.

pumpkinperson

said:All those organizations are just estimating. The GMAT has never been given to a general U.S. population sample afaik

trs

said:I believe you came close with the upper end formula but hit low on the lower end formula. Based on what I’ve read (a long time ago), the GMAT is a 6-sigma test. The median represents 115 IQ and each 100 GMAT points = 15 IQ points (15 SD scale). Therefore, 500 GMAT = 115, 600 = 130, 700 = 146 and 800 = 160. The X factor you’re not considering is that in many countries, it is easy to cheat on the math, thus the math scores (by association the total score) skew the curve. Thus, the median score goes from 500 to 550-ish. I think the GMAT score is approximately equal to half of the 1988 SAT score. Therefore, 1000 SAT = 500 GMAT = 115 IQ. 1200 = 600 =130, 1400 = 700 = 145 and 1600 = 800 = 160.

blubbalubba

said:hey pumpkinperson, why do u think mensa accepts gmat and not the gre for their admission,seems arbitrary given the multitude of tests that shows both the gre and the gmat correlate almost perfectly with one another and in some instances the gre correlates more with National iq as evidenced in a paper published by the brilliant Emil Kierkegaard: https://emilkirkegaard.dk/en/?p=7975 any thoughts?

Thanks, keep up the good work.

pumpkinperson

said:I don’t know. Maybe they think the analytical section is too coachable

Mark Gunther

said:You don’t account for GMAT scores over time. When I took it in the mid-1990’s a score of 730 was 99th percentile. From looking a the chart today, 99th percentile is 800.

pumpkinperson

said:Yes, I’m quite expert on the changes over time to the SAT. The GMAT not so much.