IQ Distribution and Standard Deviation Explained

The standard deviation: 15 (and sometimes 16)

The standard deviation of IQ is the number that controls how wide the bell is. On the modern Wechsler scales — the WAIS for adults and the WISC for children — the standard deviation is 15. That means one "step" away from the average is 15 points. A score of 115 is one step above the middle; 85 is one step below.

You will occasionally see 16 instead of 15. Older editions of the Stanford-Binet (the 1960 and 1986 versions) used a standard deviation of 16, and the Cattell Culture Fair test famously used 24. This matters because the same rarity produces a different-looking number on each scale. A top-2% result is roughly 130-132 on an SD-15 scale but around 148 on the Cattell SD-24 scale. Mensa, for example, accepts a score of 132 or higher on the Stanford-Binet or 148 or higher on the Cattell equivalent — both describe the same top slice of people. Since 2003 the Stanford-Binet switched to SD 15 to match the Wechsler scales, so today 15 is the de facto standard behind almost every published IQ classification.

The practical takeaway: an IQ number is meaningless without knowing its standard deviation. Always ask which scale a score came from before comparing it to another.

Standard deviation bands, percentiles, and rarity

Here is the core table. Because IQ is a normal distribution, the "68-95-99.7 rule" (a standard statistics fact about bell curves) tells us exactly how much of the population falls inside each band.

A percentile simply tells you what share of people you scored higher than. An IQ of 100 sits at the 50th percentile — the middle of the pack. An IQ of 115 is the 84th percentile, meaning you scored higher than about 84 out of 100 people. An IQ of 130 is roughly the 98th percentile.

Rarity is the same idea flipped around. The higher you go, the fewer people are with you:

The median: why it equals 100

In a perfectly symmetric bell curve, the mean (the average), the median (the middle value), and the mode (the most common value) all sit at the same spot. For IQ, that spot is 100. So the IQ median is 100 by design — half of all people score above it and half below.

This is a genuinely useful property. Because the median is 100, you never have to guess where "average" sits. Any score above 100 is above the halfway line, and any score below 100 is below it. There is no hidden skew pulling the middle to one side, the way income or house prices are skewed by a few extreme values.

Why extreme scores are so rare

The edges of the bell curve thin out fast, and that is not an accident — it is what a normal distribution does. Moving from the 85-115 band (about 68% of people) out to the 70-130 band adds only about 27 more percentage points of the population, even though you have doubled the width. Push out to 55-145 and you have captured 99.7% of everyone, leaving just 0.3% split between the two far tails.

That is why scores like 145 or above (roughly 1 in 741) or 160 and above (rarer than 1 in 30,000) are so uncommon. It is also why you should be skeptical of any test that hands out very high numbers freely. A legitimately extreme score is, by the math of the distribution, extremely rare — as of 2026 that has not changed, because the scale itself is defined that way.

A related caution: no single test measures your position on this curve perfectly. Every score carries a margin of error, usually a few points in either direction, so it is better to read your result as a band ("somewhere in the low 120s") than as a single exact figure.

FAQ

Q: What is the standard deviation of IQ?

A: On modern tests it is 15. The Wechsler scales (WAIS and WISC) and the current Stanford-Binet all use a mean of 100 and a standard deviation of 15. Some older tests used 16, and the Cattell scale used 24, so the same rarity shows up as a different number depending on the test.

Q: What percentage of people have an IQ over 130?

A: About 2%. An IQ of 130 sits near the 97.7th percentile on an SD-15 scale, so only about 2 to 3 people in 100 reach it. That is why 130 is the common cutoff for "gifted" and for Mensa-level qualifying scores.

Q: Is the average IQ the same as the median IQ?

A: Yes — both are 100. Because IQ is scaled to a symmetric bell curve, the mean, the median, and the most common score all fall at 100. Half of all people score above 100 and half score below it.

Q: Why do IQ scores follow a bell curve at all?

A: Because they are designed to, and because ability naturally spreads that way. Intelligence is shaped by many small independent factors that add up into a bell shape, and test makers then norm the raw scores so the population always centers on 100 with a standard deviation of 15.

References

• Intelligence quotient — Wikipedia
• Mensa International — Qualifying test scores
• The Normal Distribution and the Empirical Rule — Statistics LibreTexts

Last updated: July 13, 2026