Guide
The IQ bell curve, explained
Every IQ score sits on the same shape: a bell curve centered on 100. Once you understand two numbers, the mean and the standard deviation, you can read any score, turn it into a percentile and see how rare it is.
Want your own number? The test is 25 visual puzzles, about 12 minutes, no sign-up.
Why IQ scores form a bell curve
A bell curve, or normal distribution, is a shape where most values cluster around the middle and fewer and fewer appear as you move toward either end. IQ scores follow it because tests are designed to. Modern tests report a deviation IQ: raw results are standardized so that, within each age group, the mean is 100 and the standard deviation is 15 (Wikipedia: Intelligence quotient).
That is worth pausing on. The bell curve is not a discovery about the population that happened to come out at exactly 100. It is how the scale is defined. A test publisher gives the test to a large sample of people of each age, and then maps raw results onto this curve. Your score says where you fall relative to that sample.
Two numbers: the mean and the standard deviation
The mean is the average, the center of the curve. On the IQ scale it is 100.
The standard deviation (SD) measures spread: how far scores typically sit from the mean. On most modern tests it is 15 points. A score of 115 is one SD above the mean, 130 is two above, 85 is one below. Talking in standard deviations is useful because the shape of a normal curve is fixed: once you know how many SDs a score is from the mean, you know exactly where it sits.
The 68-95-99.7 rule
Because scores are normally distributed, a handful of proportions hold on every standard IQ test (the 68-95-99.7 rule):
- About 68% of people score between 85 and 115 (within one SD of the mean).
- About 95% score between 70 and 130 (within two SDs).
- About 99.7% score between 55 and 145 (within three SDs).
Turn those around and you get the tails: about 2.5% of people score above 130 and about 2.5% below 70, since the 5% outside the middle range splits evenly between the two sides.
Try one · Abstract Reasoning
Which tile completes the grid?
Tap the option you think is right, or show the answer.
Show the answer
The missing tile has a large hatched star (option 3).
How to solve it
- Start with the first column and name what changes from tile to tile.
- Every row and every column contains each shape (star, hexagon and square) exactly once.
- Every row and every column contains each fill (solid, hatched and outline) exactly once.
- The size (large) stays the same in every tile.
- Check the rules on the second column, then apply them to the third.
- So the missing tile has a large hatched star.
That was 1 puzzle. The full test has 25.
From score to percentile
A percentile is the share of people expected to score below a given number. It is often the clearest way to read a score, because it does not depend on which scale a test uses. The table below is computed from the normal curve with mean 100 and SD 15.
| IQ | Percentile | Rarity |
|---|---|---|
| 70 | 2.3 | 1 in 44 at or below |
| 80 | 9.1 | 1 in 11 at or below |
| 85 | 15.9 | 1 in 6 at or below |
| 90 | 25.2 | 1 in 4 at or below |
| 100 | 50 | the middle |
| 110 | 74.8 | 1 in 4 at or above |
| 115 | 84.1 | 1 in 6 at or above |
| 120 | 90.9 | 1 in 11 at or above |
| 130 | 97.7 | 1 in 44 at or above |
| 140 | 99.62 | 1 in 260 at or above |
| 145 | 99.87 | 1 in 740 at or above |
Notice how quickly rarity grows in the tails. Going from 115 to 130 takes you from about 1 in 6 to about 1 in 44. Going from 130 to 145 takes you to about 1 in 740. The curve thins out fast, which is why each extra point means more the further you are from 100. You can check any number with the IQ percentile calculator.
Same percentile, different number
Not every test uses an SD of 15. Older Stanford-Binet forms used 16, and the Cattell Culture Fair III scale uses 24 (Wikipedia: IQ classification). The percentile stays the same, but the printed number changes. A score two SDs above the mean is 130 on an SD 15 test, 132 on an SD 16 test and 148 on an SD 24 test.
You can see this in Mensa UK's published qualifying scores: 148 on the Cattell III B and 132 on the Culture Fair test, both of which are the 98th percentile on their own scales (Mensa UK). Before comparing two IQ numbers, check which scale each one is on. The percentile to IQ converter shows all three at once.
What the curve does not tell you
A bell curve describes a population. It does not make a single measurement exact. Clinical full-scale scores carry a standard error of a few points, so test manuals report a confidence interval, often around plus or minus 5 points at 95%, rather than a single value (Wechsler, 2008). A measured 120 is better read as “probably somewhere around 115 to 125”.
The curve is also a model. It fits the middle of the range well, where most people are and where tests have the most information. Far out in the tails, few people are tested and precision drops. Treat very high and very low scores as rougher estimates.
Where you sit
Your IQ Octopus result shows your estimated IQ as a marker on this same curve, with your percentile and a confidence range around it. To read more about the middle of the curve, see what the average IQ is, or browse the IQ score chart for every score from 70 to 160.
Sources
- Intelligence quotient. Wikipedia. en.wikipedia.org/wiki/Intelligence_quotient
- 68-95-99.7 rule. Wikipedia. en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule
- IQ classification. Wikipedia. en.wikipedia.org/wiki/IQ_classification
- IQ tests. British Mensa. www.mensa.org.uk/iq-tests
- Wechsler, D. (2008). WAIS-IV Technical and Interpretive Manual. Pearson.