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EnglishTwo colleagues come back from a testing session and compare results. One scored 130, the other 148. It looks like a chasm between them. In reality they performed exactly as well as each other, each just reading the result off a different scale. A 130 on a Wechsler test and a 148 on a Cattell scale (the one British Mensa uses) carry the same meaning: both people sit in roughly the top 2 percent of the population.
That is the first thing to understand about your IQ score. On its own, the number tells you very little. Without knowing which scale produced it, how wide its spread is, and how much measurement error it carries, it is a figure with no ruler behind it.
So what does your score actually say, and what do people quietly read into it that isn't there? The gap between those two things is bigger than it looks.
Where the number 100 comes from
The original IQ was calculated in a different way. In 1912 the German psychologist William Stern proposed the ratio IQ: mental age divided by actual age, times one hundred. A child of eight who solved the tasks a typical ten-year-old could solve had an IQ of 125.
For children this worked. For adults it fell apart. Mental age stops climbing somewhere around fifteen, while the calendar keeps adding years. By Stern's formula every adult would get a little "duller" with each birthday, which is nonsense.
David Wechsler fixed this in the late 1930s. Instead of comparing ages, he compared your performance against people of your own age. You take a large representative sample of the population, set its average at 100, and spread the variation around it along a normal distribution. This is the deviation IQ, and practically every serious test still uses it today.
The consequence matters. Your score is not an absolute measure of something inside your head. It is a comparison with everyone else. An IQ of 100 means you land exactly in the middle: half the population scores higher, half lower.
Plot all those results on a graph and you get a bell. Most people pile up in the middle around a hundred, and the further out you go, the thinner the ranks become. The value of 15 for the standard deviation is not a law of nature. It is a convention Wechsler chose, and other tests chose differently, which is exactly where the later confusion over numbers begins.
Bands and percentiles: where your score sits
Most modern tests use a mean of 100 and a standard deviation of 15 points, the Wechsler standard. The standard deviation decides how quickly scores thin out as you move away from the average. A single 15-point step upward shifts you from the 50th percentile to roughly the 84th.
And the percentile is more intuitive than the raw IQ. It tells you what share of the population scores below you. An IQ of 100 sits at the 50th percentile. An IQ of 115 lands near the 84th, meaning you edge out about 84 people in a hundred. An IQ of 130 already reaches the 98th, and 145 falls near the 99.9th, which works out to about two people in a thousand.
Tests then usually sort results into bands. These are approximate, and the borders between them are soft rather than sharp. Here is a common Wechsler breakdown:
| Band | IQ (Wechsler, SD 15) | Percentile | Share of population |
|---|---|---|---|
| Very superior | 130 and above | 98th and above | ~2% |
| Above average | 115-129 | 84th-98th | ~14% |
| Average | 85-114 | 16th-84th | ~68% |
| Below average | 70-84 | 2nd-16th | ~14% |
| Below 70 | under 70 | below 2nd | ~2% |
About two thirds of people fall between 85 and 115, one standard deviation on each side of the average. Roughly 2 percent climb above 130, and the same small share drops below 70. Extremes are rare precisely because a normal distribution has thin tails. Push the line another 15 points higher and the number of people who clear it drops steeply.
A percentile is easy to picture in a classroom. If you are at the 84th percentile in a room of thirty, about 25 of them score below you and four above. That sounds different from "IQ 115", but it is exactly the same fact. The percentile tells you your rank, not by how much you are better.
It is worth noticing how far apart the bands really are. The distance between 100 and 130 reads like "thirty points", when in truth it is a jump from the middle of the ladder into the top two percent. Points on the scale are not evenly spaced in terms of how many people stand between them.
Why the same performance produces different numbers
Here is the interesting part. Not every test uses a standard deviation of 15. The Cattell scale that British Mensa works with has an SD of 24, and that changes the numbers quite dramatically.
When the spread is wider, the same distance from the average is expressed in more points. The top 2 percent of the population sit around 130 on Wechsler. The very same spot on the ladder corresponds to roughly 148 on Cattell. Identical performance, a number 18 points higher.
And it isn't only Cattell. Older versions of the Stanford-Binet test used a standard deviation of 16, which puts the top 2 percent at around 132. So 130, 132 and 148 can all describe the exact same position in the ranking. Only the ruler differs, not the ability behind it.
This is why comparing scores from two different tests without naming the scale makes no sense. When someone announces "I have an IQ of 140", the first question should be: on which scale? On Wechsler that is exceptional. On Cattell it is a solid above-average result, but nowhere near as rare.
Do you know anyone who brags about a specific number from an online quiz? Most freely available quizzes have poorly calibrated norms and tend to inflate. A 135 from a five-minute test on your phone and a 135 from a professionally administered assessment are simply not the same thing.
Your score is a range, not a point
The idea that IQ is a fixed number carved in stone is probably the most widespread mistake people make about testing. Every measurement carries error, and IQ is no exception.
The technical name for it is the standard error of measurement (SEM). On a good, individually administered test it runs somewhere between 3 and 5 points. That means your "true" IQ very likely sits in a band around the measured value rather than exactly on it.
In practice, results come with a confidence interval. Measure 110 and the 95 percent confidence interval runs roughly 104 to 116. A psychologist therefore won't tell you "you have 110" so much as "your score falls in this range with 95 percent certainty". That is the more honest way to read the figure.
There is a practical upshot. If you retake the test and score 112 the first time and 108 the second, you did not get worse. Both results point to the same band, and the difference can easily come from fatigue, nerves, or plain chance. Wobbling by a few points between two sittings is completely normal.
Practice plays a part too. Sit a test again shortly after the first and you may gain a few points just from knowing the task types. Well-built tests account for this practice effect, which is one reason serious testing is not meant to be repeated from one day to the next. At the very top, uncertainty grows further: tests hit a ceiling because there are only a handful of the hardest items, so the gap between 145 and 160 rests on very little.
Even across a whole lifetime the picture holds. Deary and colleagues (2000) tracked people who had taken the same test at age 11 in the 1932 Scottish Mental Survey, then invited the survivors, by then the Lothian Birth Cohort, to sit it again in their late seventies. Most held a similar relative position across seven decades, though some shifted noticeably up or down. Your score can drift, yet your standing relative to others stays surprisingly stable.
What a band tells you, and what it doesn't
Your band reliably tells you one thing: how you stand against other people on whatever the test measures. Usually that means logical reasoning, working with patterns, verbal ability, spatial visualization, and the speed at which you process information. That is useful mainly when you want to see where your stronger and weaker areas lie.
What a band won't tell you is a longer list. Nothing about creativity, social sensitivity, motivation, or persistence. It cannot say whether you will finish a project or how you get along with people. Two people who both score 120 can lead completely different lives with completely different results.
Take two colleagues at one company. One measures 108, the other 126. On paper almost a whole band separates them. In practice the one at 108 runs the team, because he listens and decides well under pressure, while the one at 126 gets lost in detail and delivers nothing on time. The test measured something other than what that particular job needed.
None of this means IQ is useless. It is among the best single predictors of academic and work outcomes that psychology has. But it is one piece of the puzzle, not the whole picture. A high score opens doors; it does not walk through them for you. Differences inside a single band tend to be smaller than they look, too: in everyday life you will barely tell apart someone at 118 from someone at 124. A profile is more telling than one summary figure, and if you want to see your own spread across several areas, an IQ test shows not just an overall score but how your performance divides across different kinds of task.
So read your score the way you would read a position on a map, not a grade on a report card. It tells you roughly where you stand relative to other people on a handful of specific skills. What you decide to do from there is not something the number can read out for you.