IQ is, by far, the most complex and tricky stat in GURPS. This is because it gathers lots of things, and it makes it difficult to evaluate. From Kromm's homepage, IQ includes:

Adaptability (learning speed and practical problem-solving ability).
Alertness.
Analytic thinking ability (logic, reason and mathematical problem-solving ability).
Creativity (artistic or scientific innovation and imagination).
Formal education.
Memory.
Practical experience (wisdom, common sense and informal education).
Sanity (psychological stability).
Social ability.
Synthetic thinking ability (intuition).
Willpower.

Note that this article was mainly built on the IQ and DX human limits thread, especially this post from Luther (although our results slightly differ).

IQ as intellectual abilities

For our current subject, we'll strip GURPS's IQ from its secondary stats, Willpower and Perception (which removes, from the previous list, Alertness, Sanity and Willpower), in order to concentrate on something narrower and easier to evaluate.

This does not mean that we're considering pure intelligence. Comparing GURPS's IQ to a score at an intelligence test (which we'll note IK here) is still inexact. For example, the elder of a village might not be able to do simple maths, but his experience qualifies him as the highest IQ around. But still, comparing IQ and IK gives some rough idea of that person's IQ.

Kromm's very rough formula for this was: IQ = 10 + (IK-100)/20, although note that this effectively caps GURPS Intelligence at 15 for real-life humans. We'll see the actual figures later.

IQ as standard deviations from the norm

Another approach is to consider Dr. Karen Rogers studies about learning rates, and the standard deviations (SD) among a given population. A SD is a unit that represents the difference between several categories (levels) of participants for a given experience (in our case, an IK test). In the Wechsler IK tests, +15 points is +1 SD, whereas, in the Binet IK tests, +16 points is +1 SD. Here, we'll use +15 IK as the base.

According to her work, and after a few simplifications to adapt it to GURPS, the learning rate of a skill is multiplied by 3 between +0 SD (the average) and +2 SD. It's multiplied by 8 between -2 SD and +2 SD. A quick computation concludes that each +1 SD multiplies the learning rate by 1.7.

In GURPS, learning rates are determined by a skill's cost. If we consider an average skill with a score of 12, the first few levels are as below:

for an IQ of 10, the skill costs 8 points.
for an IQ of 11, the skill costs 4 points.
for an IQ of 12, the skill costs 2 points.
for an IQ of 13, the skill costs 1 point.

We don't need to go further in IQ scores because more than 99% of Earth's population is below IQ 13, according to our first estimation.

Obviously, each additional level of IQ multiplies learning rate by 2. A character with IQ 13 is learning 8 times faster than someone with IQ 10. In terms of standard deviations, this means +4 SD. This, in turn, means that +1 in IQ is +1.3 SD. This is very interesting because with Kromm's formula for matching IQ and IK we get the same result (20/15 = 1.33).

Note from vonLoringen: Child IQ is not adult IQ. Adult IK is based off one's percentile rank in the population, whereas child IQ is determined by a ratio of the child's effective age (the average age their score corresponds to) and their actual age. Thus, all IQ point deviation from 100 has to be multiplied by @2/3 to get a corresponding adult IQ. One of the links below has a calculator to do this. (Child IQ is Cattell IQ.) Dr. Rogers herself noted that she found a much larger population of high I Qs than normal (adult) statistical distribution would indicate. Given the above, the eightfold learning difference occurs between a population who, as adults, would be between 120 and 80, and thus between SD +/- 1.25, not 2.00.

Related to this is the frequently quoted IQ of 210 for Goethe. This is a Cattell IQ, based off what he could do as a child. But, his adult IQ corresponds to a 179. That is why adult scores above 200 "don't exist." Since you are being ranked against the rest of the population, you have to be a member of that population, and scores that high require a much larger population than we actually have for you to be at the top of.

I would add that, since 20 is declared upper limit of humans, wouldn't it make more sense to correspond GURPS IQ to real IQ divided by 10, since 200 is the upper limit of humans too? As the conclusion below states, 20 is the game's assigned maximum, not 15.

Caveat

Note, however, that this only takes into account a single aspect of intelligence (i.e., learning rate). We would expect a character with a high Intelligence in GURPS to not only learn faster than a character with a lower attribute, but also to make better use of what knowledge he or she did have. Accordingly, the effective difference between a -1 SD character and a +1 SD character would be the effect of learning rate plus the effect of more effective and creative use of what was learned (plus the various other factors of GURPS Intelligence). The net result is that the difference between -2 SD and +2 GURPS Intelligence characters will be larger than that observed in learning rate between -2 SD and +2 SD children.

In addition, real-world IQ corresponds only approximately to GURPS Intelligence; hence, two populations differing by 4 SD in IQ will almost certainly differ by less than 4 SD in GURPS Intelligence. (To see this, consider how the sum of two dice is only a partial predictor of the sum of three dice, and hence 2d sums that are 2 SD apart will not give rise to 3d sums that are 2 SD apart when the third uncorrelated die is added.)

The remainder of this analysis assumes that learning rate is the only effect of GURPS Intelligence; broadening the definition of GURPS Intelligence will give wider disparities between groups separated by a fixed number of Standard Deviations, and hence will tend to significantly increase the upper limit of "realistic" GURPS Intelligence scores.

Real world figures

The best adult IQ scores recorded for standardized tests tend to be at or slightly under a 200 limit. This means +6 to +7 SD. +7 SD means IQ 15.3. This sets the human intelligence limit at IQ 15, for really unique, one of kind, people.

If we map this to our population figures, we get the following results. I used the tools from this IQ page and this other one . I also used material from Audiblox and this FAQ on IQ . If you have doubts about the credibility of these websites, please add a note here.

Standard deviation	Percentage of adult population
at least -4.45	0.0005%
at least -3.25	0.069%
at least -1.95	2.9%
at least -0.65	27.43%
at least +0.65	72.57%
at least +1.95	97.13%
at least +3.25	99.94%
at least +4.55	99.9997%
at least +5.85	99.9999997%
at least +7.15	99.99999999994%

This gives us the following results for GURPS IQ.

IQ	Standard deviation	Corresponding IK	Percentage of adult population
6	-5.2 (less than -4.55)	22	0.0004%
7	-3.9 (-4.55 to -3.25)	41.5	0.06%
8	-2.6 (-3.25 to -1.95)	61	2.8%
9	-1.3 (-1.95 to -0.65)	80.5	24.5%
10	+0 (-0.65 to +0.65)	100	45.14%
11	+1.3 (+0.65 to +1.95)	119.5	25.5%
12	+2.6 (+1.95 to +3.25)	139	2.8%
13	+3.9 (+3.25 to +4.55)	158.5	0.06%
14	+5.2 (+4.55 to +5.85)	178	0.0004%
15	+6.5 (+5.85 to +7.15)	198	0.0000002%

Hint from Christian: An IK below 70 is considered a medical idiot, so an IQ of 8 (equivalent to an IK of 50-70) is to be considered hardly playable, as he is plainly: a (medical) idiot. IQ 8 should be illiterate, inumerate and have large problems coping with even easy mental activities. This might barely work for an ogre, but don't expect anything.

Contradictory Hint from Bookman: While it is true that the standard defintion of mental retardation does include, explicitly "Significantly subaverage intellectual functioning-ie, an IQ of approximately 70 or below," this does not mean that any character with a GURPS IQ of 8 should be considered unplayable, or necessarily illiterate, inumerate, et cetera. Remember that the correlation of GURPS IQ to IQ as measured by IQ tests is very loose. GURPS IQ 8 might well correspond to a person with normal or subaverage IQ (in the 70-100 range) but with deficiencies in creativity, memory, education, experience, or any of the multiple dimensions listed at the top of this article.

If you consider a town with 20,000 inhabitants (this was London's population in 1200), you get the following figures:

IQ	Nb. persons
7	12
8	560
9	4900
10	9028
11	4900
12	560
13	12
14	maybe 1
15	nobody!

Conclusion

What to do with these results, then? What do they mean?

A common misconception is that, according to those figures, 99% of characters have IQ scores between 8 and 12. This is wrong! 99% of non playing characters have IQ scores between 8 and 12. Player characters can still have higher scores, although they might have to justify them to their GM. Some GMs require an Unusual Background worth 5 to 10 points in order to be able to buy IQ at 13 or higher. Some others ask their players to buy Reputation, as people with IQ 13 or higher are pretty rare and, therefore, likely to be renown. As a general rule, a high IQ score should be taken into account in the character's background, especially if his job and/or social situation don't show that he's part of a 1% group.

Another conclusion is that diversity in the population is modeled with secondary attributes, advantages (and disadvantages), and Talents. Everybody being packed in a 4 points range doesn't mean that everybody is roughly the same! For instance, you don't have to have IQ 16 to be a Nobel prize (although it helps!). Was Einstein a pure genius, or was he "only" a genius in scientific fields? This can be reformulated as: was Einstein good at cooking or accounting (as they are also based on IQ), or just in Physics and related skills? If it's not the case, you can still model Einstein as an IQ 12 character, with a Talent in scientific skills... he'd still be the guy who invented the theory of relativity!

A third conclusion, is that creating some artificial restriction based upon erroneous comparisons with IQ tests is simply misreading the game as written. The game is written with IQ 20 as the upper end of human capability, by definition. This means that the greatest minds we would know of, people like Leonardo da Vinci and Albert Einstein, in all likelihood would have I Qs in the 18-20 range. Someone like Einstein might not have much of a cooking skill, but that's easily attributable to him not dedicating any time to developing even a default skill level in it.

(The default levels do break down at stat 16+, this is why the suggestions of basing default skill off of Stat/2 or alternately having Stat 16 as max base for default have been around since the early days.)