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Intelligence quotient (IQ): definition, measurement, history, and uses

A concise encyclopedia article on intelligence quotient (IQ): what it measures, common tests, historical origins, interpretation, applications, controversies (heritability, Flynn effect) and high-IQ groups.

Author: Leandro Alegsa Creation date: November 13, 2022 Last updated: June 7, 2026

en.wikipedia.org · Public domain

The intelligence quotient, commonly abbreviated IQ, is a numerical value intended to represent certain aspects of a person’s cognitive ability. An IQ is obtained by administering one of several standardized tests that evaluate problem solving, reasoning, memory, processing speed and related skills. The result is reported as a single number that places an individual relative to the performance of a reference group.

What IQ tests measure and how scores are scaled

IQ instruments aim to assess general intellectual functioning rather than specific learned facts. They typically include a mix of verbal, nonverbal, quantitative and spatial items designed to minimize dependence on particular schooling or cultural knowledge where possible; nevertheless, test content and administration can still be influenced by language and background. Scores are scaled so that the population distribution conforms approximately to a normal distribution (bell curve), with a chosen central value (commonly 100) and a standard deviation that determines how spread out scores are. Different test batteries use particular norms and scaling procedures; for example, widely used adult instruments generate composite scores and subtest profiles to show strengths and weaknesses.

Common tests and typical uses

Several well-known tests have been developed over the 20th and 21st centuries to estimate intelligence across ages and abilities. These include group-administered and individually administered batteries designed for children and adults. Practitioners and researchers use IQ scores for varied purposes, such as:

screening and diagnostic work in educational assessment and special-needs planning;
occupational guidance and personnel selection in some contexts;
population-level studies of cognitive trends and public health research;
psychological evaluation combined with other clinical information to inform treatment and supports.

IQ scores are a statistical indicator rather than an absolute label: they are most informative when interpreted alongside academic records, functional assessments and background information.

History and scientific context

The effort to quantify individual differences in mental ability traces to the late 19th and early 20th centuries. Early thinkers such as Francis Galton promoted measurement of cognitive and sensory traits; later, formal testing approaches were developed to assist educational placement and to study development. Over time, psychologists refined methods for item construction, norming and reliability. Research has also linked cognitive test performance to later-life outcomes: longitudinal analyses have associated lower scores on cognitive batteries with increased risk of certain age-related conditions in some studies, including dementia-related outcomes, though these relationships are complex and influenced by many factors.

Controversies, heredity and population trends

IQ has been the subject of substantial debate. One long-standing question concerns the relative contributions of genetics and environmental factors (family background, education, nutrition, and social context) to individual differences in IQ. Scientific consensus recognizes that both heredity and environment play roles, but estimates of their relative influence vary across studies and depend on age and circumstances. Another debated observation is the Flynn effect, the well-documented rise in average test scores observed in many countries during much of the 20th century; scholars discuss whether this reflects true changes in underlying cognitive ability, improvements in test-taking skills and education, or methodological factors in testing and sampling.

IQ scores are useful but limited. They provide a snapshot tied to particular tasks and testing conditions, and they do not capture all forms of intelligence, creativity, practical skills, emotional reasoning or moral judgment. Scores are correlated with some life outcomes—such as educational attainment and, in aggregate, aspects of socioeconomic status including parental social position—but they are only one factor among many. Ethical and equitable use of IQ testing requires careful administration, culturally sensitive interpretation and attention to the stakes for individuals.

Communities and further resources

People who perform at the high end of standardized tests sometimes form organizations that connect members and promote research and outreach; an example is Mensa International. For further reading on tests, measurement theory and public debate, consult introductory texts and authoritative reviews accessible through academic and professional resources; specialized sources include test manuals and peer-reviewed literature accessible via curated portals such as psychological measurement overviews and institutional repositories. For general overviews and guidance on interpreting IQ results, see materials on test design and administration available from educational and clinical psychology providers (IQ resources) and comparative reports on cognitive assessment and population studies.

Responsible use of IQ testing emphasizes transparency about what is measured, proper norming, and combining test results with broader contextual information to support individuals' educational and clinical needs.

IQ tests are constructed so that the results are approximately normally distributed for a sufficiently large population sample. Color-coded ranges each correspond to one standard deviation.

Calculations

Historical

Alfred Binet, who developed the first useful intelligence test in 1905 with the Binet-Simon test, specified mental ability as the age of intelligence. The test consisted of tasks with increasing difficulty, which should be solvable as clearly as possible for the respective age groups. Example: An averagely developed eight-year-old should be able to solve all tasks of his age group (and below), but not the tasks of nine-year-olds. If a child did not manage all the tasks of its age group, it had a lower, if it also managed tasks of the higher age group, it had a higher "intelligence age".

William Stern put this age of intelligence in relation to age and thus invented the intelligence quotient at the University of Breslau in 1912.

Lewis M. Terman of Stanford University further developed the Simon and Kinte quotient translated by Goddard from French into English. To remove the decimal places, he multiplied the intelligence age-life quotient by 100.

${IQ}={\frac {{\text{Intelligenzalter}}}{{\text{Lebensalter}}}}\times 100$

Modern

Since the age of intelligence increases more slowly than the age of life, the IQ according to Stern's formula consistently decreases. Terman also recognized this problem in his further development. To address this problem, he normalized the test for different age groups. He adjusted the distribution to a normal distribution for each age. In the Stanford-Binet test developed in 1937, the standard deviation varies between 15 and 16 IQ points depending on age (cf. Valencia and Suzuki, 2000, p. 5 ff.).

The IQ calculation originally developed only for children, specifically for school readiness tests, was later extended to adults by David Wechsler by applying population-based scaling with a mean of 100. Today's deviance IQ scale has a mean of 100 and a standard deviation (SD) of 15. It is used, for example, in the Hamburg-Wechsler intelligence test series. Since IQ is overestimated in the public as a "label" of persons, for example, in terms of stability and universality, some tests deliberately use other norm scales.

Conversions

It is also possible to specify other norm scales, such as percentile rank. By referring to the normal distribution, values from other scales can be converted into an IQ scale with a mean value of 100 without loss of information:

${IQ}=100+15\times {\frac {(x-\mu )}{\sigma }}$

(See also Standardization (Statistics)). Thereby mean

determined scale value in the test used
$\mu$ mean value of the scale used
$\sigma$ standard deviation of the used scale

Example

The IST-2000 uses what is known as the Standard Score (SW) scale, which has a mean of 100 and a standard deviation of 10. If a person has scored a standard score of 110, this can be converted to a standard IQ score as follows:
Inserted:
${IQ}=100+15\times {\frac {(110-100)}{10}}=115$

Since 110 of the standard value scale is exactly one standard deviation above the mean, the same must apply to the AW-IQ value. And, as calculated, this is also true with a value of 115. An AW-IQ value of 85, which is exactly one standard deviation below the mean, corresponds to an ACTUAL value of 90 (see also Linear Transformation).

Reliability and measurement error

When interpreting results, the measurement error and the error probability to be accepted must be taken into account (cf. error of the first kind). The probability of error determines the length of the confidence interval. The latter is influenced by the necessary certainty of the diagnostic decision to be made.

In 2014, the US Supreme Court had to decide up to what IQ an offender should be considered insane and therefore not be executed in the case of a death sentence. In this case, the American Psychological Association and the American Association on Intellectual and Developmental Disabilities argued that IQ tests have a margin of error of 10 points up and down.

Intelligence tests must be periodically rescaled (or the validity of the norms checked) to keep the average score at 100. Until the 1990s, IQ tests in industrialized countries had shown a steadily rising average. There is no consensus on the cause of this "Flynn effect," such as a more evenly distributed schooling or the informative influence of mass media. The numerical values are not comparable without knowledge of the underlying test and its normalization. The guideline value for the test is eight years, which is suggested in DIN 33430 for the field of aptitude testing.

Questions and Answers

Q: What is an intelligence quotient (IQ)?

A: An intelligence quotient (IQ) is a number which is the result of a standard test to measure intelligence.

Q: Who developed the idea of measuring intelligence?

A: The idea of measuring intelligence was developed by British scientist Francis Galton in his book Hereditary genius published in the late 19th century.

Q: How does IQ measure a person's score?

A: IQ measures a person's score comparatively, telling how much above or below average they are.

Q: What modern IQ test is used today?

A: The Wechsler Adult Intelligence Scale is one modern IQ test used today. It states where the subject's score falls on the Gaussian bell curve with a center value of 100 and standard deviation of 15.

Q: What other aspects can be predicted from an IQ score?

A: An IQ score can predict other aspects such as onset of dementia and Alzheimer’s disease, social status, and educational achievement or special needs up to 11 years later.

Q: To what extent is IQ inherited?

A: There is still disagreement about to what extent IQ is inherited; some believe it depends on both genetics and environment while others disagree.

Q: How have average IQ scores changed over time?

A: Average IQ scores for many populations have been rising about three points per decade since the early 20th century due to something called the Flynn effect.