Okay, I know that it’s a questionable concept, but …
It’s idle curiosity. What is the population frequency of different “IQ” numbers? It’s fairly obvious that 100 is the mean value, and on an IQ-related test such a person would score in the 50th percentile. So what are the percentiles for higher scores? Common ones, like 110, 120, 130 - it seems intuitive that they would be 60th, 70th, etc. But that doesn’t make sense to me. Where does 99th percentile kick in?
I don’t recall nearly as much as I should about statistics, but surely a “normal” curve is involved, because the farther you get from the mean, the fewer instances?
And, to answer the OP, yes a “normal” bell curve is involved, to an extent. But to know the exact numbers, like pinkfreud has already pointed out, you would need to specify which test. Contrary to popular belief, the only score that is “standard” is 100, and that’s only be definition, not design.
To qualify for Mensa I had to take two IQ tests. I scored 158 on the first one, which ranked me in the top 2%.
I scored 139 on the second one, which ranked me in the top 1%.
So, you can see there’s quite a disparity among the scores.
And as you can see, they are not perfect, since one told me I was dumber than the other.
IQ scores are normally distributed with a mean of 100 and a standard distribution of 15. Look up “bell curve” or Gaussian curve" to get specifics on percentiles.
lorinada, I know what you mean. Test I took in elementary school showed a fairly impressive number. Decent results (for the era - antediluvian) on my SAT, and good results on my GRE - especially considering my age at the time. Then, in 1998, a psychologist gave me one. I was fairly incensed when he said my score was 140. Then he said it was the highest score possible on that test. :dubious: Would that have been the WAIS test, maybe?
I guess it was all those years of 99th percentiles, and wondering where intermediate kinds of results placed people.
This is 100% incorrect. There is some misinformation is this thread. Most IQ tests are designed with a certain mean and standard deviation. The mean is almost always 100 and the standard deviation is usually 15 but sometimes 10.
What you want to do is calculate a z-score. This tells you the area under the normal curve for a given score based on the mean and standard deviation.
The formula for a z-score is:
(IQ Test Score - Mean) / Standard Deviation
For a test score of 130, that gives us (130 - 100) / 15 = 2.0
A z-score of 2.0 = 0.9772. That means that an IQ score of 130 is in the 97.7th percentile.
Try it for yourself a few times. Use score below the mean to get negative z-scores. You will quickly see why most of the people that claim to have IQ’s of 150 or more are probably lying. An IQ score of 150 is in the 99.95th percentile. Not impossible but you shouldn’t have three people at the same dinner party with IQ scores that high.
No joke. The probability of having three people in the same room (unless they’re relatives, maybe) with scores that say they’re one in 5,000(? my math ability pretty much got up and went after the second closed-head injury) is, um, extremely remote. Especially given that each of the individuals is fairly improbable.
I used to be a Mensa test proctor. One of the tests I administered was the Cattell 3. An applicant who made a score of at least 148 on the Cattell 3 was in the top 2%, and thus was eligible to join Mensa. Lots of Mensans (probably most of 'em) have IQs in the 150 range, if the Cattell is the test being discussed. As I said in my first post above, unless you specify which test, it’s not very meaningful to talk about percentile ranking for a certain score.
Very true. However, most people mean one of the major IQ tests with a mean of 100 and standard deviation of 15 when they brag about their IQ score. We have had people on these boards claim IQ’s of 170 and higher. Calculate a z-score for that and decide how likely that is for yourself.
In any case, it only takes a few seconds to calculate a z-score and look up the percentile for any test once you know that basic information. I think any educated should know how to do it because it pops up everywhere and not just with IQ tests.
For instance, the old SAT was supposed to have a mean of 1000 and a standard deviation of 100 (those were imperfect in practice). Students and parents would look at a score of 1300 and then at a 1400 and figure that it was only a 100 point difference. Literally that was true but what was much more important was that there was a whole standard deviation difference between the two. That is huge and can be seen on a z-score chart.
Yup, IQ scores theoritically fall into a specialized curve called the bell/Gaussian/normal distribution curve.
It seems that everyone I’ve met claims to have an IQ above 130 or so. However, only a very few people (fewer than I can count with the fingers on my hands) have borne that out in their abilities–one of them, for example, put off essays & papers off until the morning of the due date and could type it straight out over an half hour to an hour, very little editing, it all came from his fingers instantly… and he got the highest score from the professor. (What about citations and footnotes? He invented them. That’s right, he invented them and no one cross-checked them.) Now that’s what I’d call one-in-a-thousand feat. :eek:
I’ve always found it misleading to think about IQ in terms of rarity in any sort of practical sense. Obviously, social forces cause people with high IQs to come together. (i.e. IQ is not randomly distributed). So, in one place, everybody in the room is a 1-in-1000, and then in other places, triple digits IQs are few and far between, so a 1-in-1000 is for practical purposes a 1-in-25,000.
I’d like to see map of the US with the IQs plotted, to try and localize those percentiles.
You are right that IQ’s are not randomly distributed in terms of geography but it is probably on a much smaller scale than you figured. The average IQ of Cambridge, MA (where Harvard and MIT are located) is probably higher than that of Dorchester. A lot of college areas would be that way too. Most of the time however, you would need to be way more specific than that to get meaningful difference. It may just be an upscale neighborhood versus an impoverished neighborhood in a town.
I am not sure what would happen if you gave an IQ test to every person in the country and mapped it. Minority populations tend to score lower on IQ tests so areas with high minority populations would tend to have lower mean IQ test scores.
I can say that all IQ levels would be present in all populations. I come from a very small, poor town in Louisiana and I scored pretty well on IQ tests and many other students did too despite the circumstances.
*I’ve always found it misleading to think about IQ in terms of rarity in any sort of practical sense. *
Yes, and you’ll find buried chests of gold in the beach more often than you’ll find buried chests of gold in the Antarctica. It only merely increases your chances of finding an extremely, extremely rare occurence–it might be two standard deviations instead of three, but two standard deviations are still huge.
Sorry, it’s a pet peeve of mine. It is simply statistically impossible that all my coworkers and IRL friends and family members have an IQ of 130 or above, period, as well as seemingly everyone’s that posted in a message board IQ thread in every single message board I’ve encountered.
is, um, extremely remote. Especially given that each of the individuals is fairly improbable. 