Skip to content

How an IQ Score Is Calculated: Deviation Scores, Not Raw Right Answers

An IQ score is not a count of correct answers. It is a rank inside a norm sample, rescaled so the average is 100. Here is each step of that conversion.

By Published Updated 5 min read

Reign Creative LLC makes IQ Test & Brain Training Games, which this article links to, so we have a commercial interest in it. How we write and check articles.

Key takeaways

  • A raw score — the number of items answered correctly — is never reported, because it has no meaning until it is compared with how a reference group performed on the same items.
  • Raw scores become scaled scores, scaled scores are summed, and the sum is converted to a standard score on a scale with a mean of 100 and a standard deviation of 15. That is what 'deviation IQ' means.
  • The mean of 100 is imposed by the conversion, not discovered in the data. So is the standard deviation of 15.
  • Because the scale is pinned to a norm sample, a score expires. The WAIS-5 was published in 2024 with updated norms; a score from an older edition was a rank against a different group of people.
  • Every reported score carries measurement error, which is why a competent report gives a confidence interval rather than a single number.
  • Our own app, IQ Test & Brain Training Games, offers an IQ-style test alongside its games; its listing describes no norm sample and calls the results estimates based on app activities, not a professional assessment, so read them as a record of how you did on the app's questions rather than as a deviation IQ.

An IQ score is not a count of correct answers and it is not a percentage. It is produced by looking up how a person's raw performance compares with a reference group of the same age, and then rescaling that comparison onto a fixed metric — conventionally one with an average of 100 and a standard deviation of 15. The number tells you about a position in a distribution, which is why it can exist at all without anyone knowing how many questions were on the test.

That is the core of it. The rest of this article walks the conversion, step by step, and names the two places where most confusion enters.

Step one: the raw score, which nobody reports

Every subtest produces a raw score — items correct, sometimes weighted for speed or quality of response. On its own that number is uninterpretable. Twenty-three correct is good or bad depending entirely on what the items were and who else attempted them.

This is a general property of norm-referenced measurement, not a quirk of cognitive testing. A raw score becomes informative only when attached to a distribution. That attachment is the entire technical content of a test's norms.

Step two: scaled scores, one per subtest

The publisher administers the battery to a standardisation sample chosen to match a defined population on characteristics such as age, sex, education and region. For each age band, the distribution of raw scores on each subtest is recorded.

A new test taker's raw score is then converted, through published tables, into a scaled score — a position within that age band's distribution. Two people with identical raw scores but different ages can receive different scaled scores, because they are being compared with different groups. That is the design working as intended, not a flaw.

Step three: the composite, and the deviation metric

The relevant scaled scores are summed, and the sum is converted — again by table — into a composite standard score.

The metric is where the familiar numbers come from. Wechsler-type scores are expressed on a scale with a mean of 100 and a standard deviation of 15; a 2026 meta-analysis of Wechsler profiles states the convention explicitly when describing how it standardised effect sizes against a control with a mean of 100 and a standard deviation of 15. Under that metric:

  • 100 is the centre of the comparison group by construction
  • 115 sits one standard deviation above it
  • 85 sits one standard deviation below it
  • 130 sits two standard deviations above it

Called a deviation IQ, this replaced an older ratio idea in which a "mental age" was divided by chronological age. The replacement matters because a ratio breaks down in adulthood, where chronological age keeps rising and task performance does not.

Pearson's own description of the Wechsler Adult Intelligence Scale, Fifth Edition shows how much structure sits on top of that single composite: the battery covers ages 16:0 to 90:11, draws its Full Scale IQ from seven core subtests, and reports a General Ability Index plus a large set of ancillary index scores alongside five domain scores. The composite is a summary of subtests, and the subtests are where the information is.

Why the average is 100 by construction

This is the point most worth carrying away. The mean of 100 is not an empirical discovery about human beings. It is imposed during step three, and re-imposed every time an instrument is renormed against a fresh sample.

The mathematics underneath is the normal distribution, which the NIST/SEMATECH statistical handbook describes with two parameters: a location parameter, the mean, and a scale parameter, the standard deviation — with the standard normal case being mean 0 and standard deviation 1. Setting the location to 100 and the scale to 15 is a rescaling of that standard case. Nothing about people forces those two numbers; they are units, like choosing Celsius over Fahrenheit.

Two consequences follow immediately. First, "the average IQ is 100" is close to a tautology. Second, a score is dated: it is a rank against the particular sample used to build the tables. The WAIS-5 was published in 2024 with updated norms, and a score from an earlier edition was a comparison with a different set of people. Our companion article on why the average IQ score is always 100 follows that thread into what happens at renorming.

Where the error bar comes from

A calculated score still is not an exact quantity. ETS's plain-language guide to reliability puts the underlying idea simply: scores are reliable to the extent that they are consistent across different occasions of testing, different editions of a test, and different raters scoring the same responses. Inconsistency across those conditions is measurement error, summarised by the standard error of measurement.

In practice this is why a report from a qualified administrator gives a band rather than a point. A composite reported as a single tidy integer has thrown away information the test itself supplies. The distinction between the score, its percentile equivalent and the interval around it is worked through in percentile, standard score and raw score.

What our app's number is, and what it is not

IQ Test & Brain Training Games is our own app, and it shows numbers of two kinds: game results such as personal bests, accuracy and streaks, and the results of its IQ-style test, memory test and reaction time test.

The game score is points. A correct answer earns a base value, with a bonus for answering quickly and a further bonus for an unbroken streak, the whole thing scaled by the difficulty you selected. The design goal is to make a fast, accurate, sustained run feel different from a slow, patchy one — which is a game design goal, not a measurement goal.

A higher game score says only that you did better at that mode, at that difficulty, than you did before. For the IQ-style test, the listing describes no standardisation sample, age band or conversion table, and it states that IQ test and other results are estimates based on app activities, not medical, psychological, clinical, educational-placement, employment or professional diagnostic assessments. Nobody supervises the sitting either, so whatever form a result takes, it is not the deviation IQ this article describes. The honest, useful readings are accuracy on a fixed mode and difficulty, and response time — the kind of self-comparison discussed in our guide to building a daily practice habit.

Keeping practice separate from standardised psychological assessment is not modesty. It is the difference between a number that means something because of how it was built, and a number that means something because of what you did last Tuesday.

Reading the conversion backwards

If you know only the composite, you know only a rank. You do not know which subtests carried it, how variable the profile was, how much error surrounds it, or which norm sample it was pinned to — and each of those can matter more than the headline figure.

That is the practical value of understanding the calculation: it tells you which follow-up questions are worth asking. Start with what IQ tests actually measure for the construct behind the arithmetic, browse the IQ tests and reasoning hub for the rest of the series, or open the education and brain training section for practice-side material.

Good to know

Frequently asked questions

How is an IQ score calculated?
Each subtest's raw score is converted into a scaled score using tables built from a norm sample of people the same age. The relevant scaled scores are summed, and that sum is looked up in a further table which converts it into a standard score on a scale centred on 100. No step involves dividing correct answers by total questions.
What does 'deviation IQ' mean?
It means the score expresses how far a person sits from the average of their age group, measured in standard deviations, rather than as a ratio of mental age to chronological age. On the common metric, a mean of 100 and a standard deviation of 15, a score of 115 is one standard deviation above the comparison group's average.
Why is 15 the standard deviation?
It is a convention, chosen and then applied during the conversion. Different instruments have historically used different spreads, which is one reason two scores from two publishers are not directly interchangeable. On a scale with a mean of 100 and a standard deviation of 15, the familiar landmarks — 85, 115, 130 — are simply one and two standard deviations from the centre.
Does a brain training app calculate an IQ score?
Ours, IQ Test & Brain Training Games, offers an IQ-style test, so it does produce a result — but its Google Play listing describes IQ test results as estimates based on app activities, not medical, psychological, clinical or professional diagnostic assessments. The listing describes no norm sample or conversion table of the kind explained in this article, so treat the result as a record of how you did on the app's own questions, not as a deviation IQ.

Sources

  1. WAIS-5 — Wechsler Adult Intelligence Scale, Fifth Edition (opens in a new tab)Pearson Assessments (Pearson Clinical Assessment US) — accessed
  2. Test Reliability — Basic Concepts (Research Memorandum RM-18-01) (opens in a new tab)Educational Testing Service (Samuel A. Livingston, 2018) — accessed
  3. 1.3.6.6.1. Normal Distribution (NIST/SEMATECH e-Handbook of Statistical Methods) (opens in a new tab)National Institute of Standards and Technology — accessed
  4. Cognitive Profile of Autism and Intellectual Disorder in Wechsler's Scales: Meta-Analysis (opens in a new tab)European Journal of Investigation in Health, Psychology and Education, via PubMed Central — accessed

About the author

— The independent app studio that builds the apps covered on this site and publishes every article here. On Google Play it publishes as Reign Collective Apps.

We use AI tools to help research, draft and edit our articles. Each article lists the sources its factual claims rely on, and details about our apps come from their live Google Play listings. No article on this site has been reviewed by an independent expert unless the reviewer is named on it.

Spotted an error? Tell us — how corrections are handled is set out in our editorial policy.

Keep reading