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What an IQ of 120 Means, and What It Does Not

On the scale most modern tests use, 120 sits around the 91st percentile. Change the scale and the same number moves. Add the measurement error every test carries and it stops being a point at all.

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What you need to know

  • Most modern tests place scores on a scale with a mean of 100 and a standard deviation of 15. On that scale, 120 corresponds to roughly the 91st percentile.
  • Older and alternative scales use a different standard deviation — 16 on some Stanford-Binet forms, 24 on the Cattell scale — so the same printed number means a different standing.
  • Every score carries measurement error. A responsibly reported result is a range several points wide, not a point, and two scores inside that range are not meaningfully different.
  • A percentile is a position in a reference sample, not a fixed rank among people. It moves when the reference sample changes or ages.

Someone tells you their IQ is 120. Before that means anything at all, you need three further pieces of information: which scale, measured against whom, and with how much error. Without them the number is a decoration. With them it is a reasonably precise statement — and a narrower one than most people assume.

The scale

Modern IQ scores are what psychometricians call deviation scores. They are not a ratio of anything. The test is given to a large reference sample chosen to represent a population, the raw results are arranged so the average is set to 100, and the spread is set so that one standard deviation equals a fixed number of points. Standard deviation is simply a measure of how spread out the scores are: on a scale where it is 15, roughly two in three people fall between 85 and 115, and roughly 19 in 20 fall between 70 and 130.

On that mean-100, standard-deviation-15 scale, a score of 120 is one and one-third standard deviations above the average, which places it at approximately the 91st percentile of the reference sample. Not the 95th, not “top 5%” — approximately the 91st, meaning roughly nine people in a hundred in that sample scored higher.

Change the scale and the number moves

  • Mean 100, standard deviation 15 — the Wechsler scales and most contemporary tests. 120 is about the 91st percentile.
  • Mean 100, standard deviation 16 — some Stanford-Binet forms. The same 120 is a slightly smaller distance above average, so it sits a little lower.
  • Mean 100, standard deviation 24 — the Cattell scale, used by some high-IQ societies. A 120 here is well under one standard deviation above average, nowhere near the 91st percentile.
  • Ratio IQ — the historical formula of mental age over chronological age. It has not been used in serious testing for generations, and childhood figures quoted in that form do not convert cleanly to a modern score.

This is why a printed number without its scale is close to meaningless, and why comparing two people’s scores from two different tests is a conversion problem, not a subtraction problem.

A score is a position in a specific reference sample on a specific scale — not a quantity of anything you carry around.

The error is not a technicality

No test measures without error. Test manuals publish a figure called the standard error of measurement, which describes how much a person’s observed score is expected to bounce around their true standing across repeated sittings. That is why a responsible report gives a confidence interval — a range within which the true score most likely lies — rather than a bare number.

The practical consequence is blunt: two scores a few points apart are usually indistinguishable. A 118 and a 122 are the same result. Someone whose score moved from 116 to 121 between two sittings has not improved; they have produced two estimates from the same band, which is what the band is for.

Courts have had to reason about exactly this. In Hall v. Florida the US Supreme Court addressed the use of a rigid IQ cutoff in determining intellectual disability and held that measurement error has to be taken into account rather than treating a single reported score as an exact figure. When the consequences are that serious, the confidence range stops being a technicality.

What 120 does not tell you

  • It does not describe any specific skill. It is a summary of performance across subtests that measure different things, and two people with the same total can have very different profiles.
  • It does not predict an individual outcome. Test scores relate to group averages in education and work; the spread around those averages is wide enough that any single prediction is weak.
  • It does not measure motivation, conscientiousness, judgement, creativity or knowledge of a field, all of which matter and none of which the score is built to capture.
  • It does not stay fixed against an ageing reference sample. Norms expire, and a percentile computed against a sample from decades ago quietly drifts upward.
  • It does not mean the same thing at 8 and at 48. Age-referenced scores compare you with your own age band, not with everyone.
Your own number

Where would your own score land?

A number worth keeping comes with the three things above attached: the named scale it was measured on, the percentile against a stated reference sample, and the confidence range around it. If a result gives you a single figure and nothing else, the missing information is not a detail that was left out for simplicity — it is the part that would have let you check the claim.

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None of this makes 120 uninteresting. On the standard modern scale it is a solidly above-average result, comfortably above the middle of the distribution and a long way from either extreme. It is simply a narrower statement than the internet treats it as: on this scale, against this sample, on this day, within this range.

Common questions

Is an IQ of 120 high?

On the scale most modern tests use — mean 100, standard deviation 15 — it is clearly above average, at approximately the 91st percentile of the reference sample. It is not in the range usually described as very superior, and on a scale with a larger standard deviation, such as the Cattell scale used by some societies, the same printed number sits considerably lower.

Why do two tests give me different numbers?

Three reasons, all normal. They may use different scales. They may be normed on different reference samples. And every test carries measurement error, so repeated sittings scatter around your true standing. Differences of a few points are expected rather than surprising.

What percentile is 120?

Roughly the 91st on a mean-100, standard-deviation-15 scale — about nine people in a hundred in the reference sample scored higher. On a standard-deviation-16 scale it is slightly lower, and on the standard-deviation-24 Cattell scale it is far lower. The percentile follows the scale, not the number.

Sources for this story

  1. Technical and interpretive manuals for the Wechsler intelligence scales, covering scaling, norming and the standard error of measurement — Pearson
  2. Standards for Educational and Psychological Testing, on score reporting and confidence intervals — American Educational Research Association, American Psychological Association and National Council on Measurement in Education
  3. Hall v. Florida (2014), on rigid IQ cutoffs and measurement error — Supreme Court of the United States
  4. Public guidance on psychological testing and assessment — American Psychological Association

Corrections: spotted an error? Email corrections@iqmetrics.org and we will update this story and note the change here.

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Filed under#percentiles and norms#wechsler scales#scores and scales#confidence intervals

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