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What a specific number means on a specific scale, why every score needs a confidence range, and how the scales convert.
The first IQ scores came from dividing mental age by chronological age. The formula worked reasonably well for children and produced nonsense for adults — which is exactly why every major test replaced it.
A score of 160 is four standard deviations above average — about one person in 31,560. The sample the score is measured against holds roughly 2,200 people, which is why the top of the table is calculated rather than observed.
A Full-Scale IQ is an average of several narrower index scores, and when those indexes disagree by enough, the average describes none of them well.
Every properly built test publishes a standard error of measurement alongside the score. On a mean-100, standard-deviation-15 scale it is large enough that a reported 104 and a reported 111 are not reliably different results.
Wechsler scales use a standard deviation of 15, older Stanford-Binet forms used 16, and the Cattell scales use 24. One standing prints as three different numbers — and one printed 140 is a one-in-260 result on one of those scales and a one-in-21 result on another.
Mensa admits at the 98th percentile of a supervised, properly normed test. That single rule produces a different qualifying figure on every scale — and none of them is the 130 the internet keeps repeating.
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.
An IQ figure is meaningless without the scale it was measured on and the range around it. Every story here reports all three, or says plainly that the source did not.
Each story ends with the studies, datasets and documents it draws on, named and attributed, so you can go and read them yourself.
Spotted an error? Write to corrections@iqmetrics.org. Corrections are made on the story and noted at the bottom of it — never quietly.
Our IIF-certified assessment reports your score with its scale, percentile and confidence range — and a breakdown of the cognitive domains behind it.
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