How IQ Tests Are Normed: Who Sets 100, and Why It Matters for Your Score

One raw score, two norm groups: a worked example

The same raw score earns different IQs under different norm groups, because the IQ depends on the group’s average and its spread.

Take 14 correct answers out of 20. IQMog’s published conversion treats 10 correct as the average and 5 correct answers as one standard deviation, so z = (14 − 10) ÷ 5 = 0.8 and IQ = 100 + 15 × 0.8 = 112. That is the same as IQ = 70 + 3 × 14.

Now score the same 14 against a group that averages 12 correct with a standard deviation of 4. Then z = (14 − 12) ÷ 4 = 0.5 and IQ = 100 + 15 × 0.5 = 107.5. The answers are identical and the IQs sit 4.5 points apart. Only the group changed.

Read the table from the top: the stronger the comparison group, the lower your IQ for the same answers. Once the group is fixed, the IQ score chart shows where each IQ sits on the bell curve.

How big is a norm group, and who is in it?

Professional IQ tests use norm groups of a few thousand people, built to mirror the national population on age, sex, region, education and ethnicity.

Size matters per age band. The WAIS-IV uses 200 people in each age band from 16 to 69 and 100 in each band from 70 to 90 (Pearson), and each age-specific table rests on those counts. The CFT 20-R went further and checked its norms with a second sample of 870 people in 2015 (Hogrefe).

Norm groups have grown with the field. The 1937 Stanford-Binet revision used 3,200 examinees aged 1 year 6 months to 18 years, while the SB5 reached 4,800 people up to age 96 (Roid and Barram). A national test also uses a national group: the CFT 20-R is normed in Germany, the WAIS-IV in the United States. How old the Stanford-Binet norms are next to the newer ones is covered in the Stanford-Binet guide, and the Wechsler tests page covers the WAIS family.

Are IQ tests “white normed”?

The major US clinical tests are not normed on one group: the WAIS-IV and SB5 samples were stratified by race and ethnicity to match the US population.

The WAIS-IV sample was stratified by age, sex, ethnicity, education and region (Pearson), and its tables closely match the October 2005 US Census (Canivez, 2010). The SB5 used ethnic categories that include African-, Asian-, Anglo/Caucasian- and Native American and Hispanic, matched to 2001 Census percentages (Roid and Barram). The WAIS-IV sample also excluded people with certain language, sensory and motor limitations, so its “population” means people able to take the test as designed.

Matching tells you who is in the sample and sets one national average at 100 for everyone. It does not decide whether each item works the same way for every group, which is a separate question about item fairness, and no norm table answers it.

Why do old norms inflate scores?

When scores rise across generations, old norms inflate scores because the older group sets a lower bar for 100.

A meta-analysis of 271 samples and almost 4 million people from 1909 to 2013 found full-scale IQ scores rising about 0.28 points a year. Fluid tests rose 0.41 points a year and crystallized tests 0.21 (Pietschnig and Voracek, 2015). Multiply by the age of a norm group and you get its drift.

At the study’s historical full-scale rate, a norm group 15 years old adds 4.2 points, so someone who averages 100 against today’s group reads about 104 against it. Matrix puzzles such as Raven’s are a fluid-reasoning format, which puts them in the faster column: 6.2 points over 15 years. Pearson collected fresh WAIS-5 norms in 2023–2024 (Pearson) for this reason.

That drift is why publishers collect fresh norms with each new edition. How scores shift across birth years is covered in how IQ scores drift across decades.

Why does measurement error matter as much as the norm?

The norm decides where 100 sits, and measurement error decides how far any single score can wander around its true value.

The US Supreme Court made this point in Hall v. Florida (decided 27 May 2014). Florida treated an IQ above 70 as the end of the inquiry. Freddie Hall scored 71, and the opinion notes that 71 “is generally considered to reflect a range between 66 and 76 with 95% confidence”. The Court held that the state’s rigid threshold, as the Florida Supreme Court applied it, is unconstitutional because it ignored the test’s standard error of measurement (Hall v. Florida, 572 U.S. 701).

How does IQMog turn answers into a score?

IQMog turns answers into a score with a fixed, published conversion: IQ = 70 + 3 × the number of correct answers out of 20.

The reference is set by rule. Ten correct answers is the average and 100, and 5 correct answers is one standard deviation, which is 15 points, or 3 points per answer. Zero correct gives 70 and 20 correct gives 130, the top of the scale. Around your estimate you get a score range of about ±12 points (95%), worked out from an assumed reliability of 0.82.

Because the rule is public, you can recompute your own result in a few seconds: count the right answers, multiply by 3, add 70. A measured norm group would replace the rule that 10 is the average with a measured average, and the arithmetic after that stays the same. Every step of IQMog’s scoring formula is on one page.