What is IQ? A standard score, a scale, and what the number means

0 Quick Answer

An IQ is a standard score that expresses how a person performed on a normed intelligence test relative to a reference sample of their age, on a scale with a mean of 100 and a standard deviation of 15, so that 100 is the middle of the reference group, 115 is one standard deviation above it at about the 84th percentile, and 130 is two above it at about the 98th. The letters stand for intelligence quotient because the first version of the number, proposed by William Stern in 1912 and adopted by Lewis Terman in 1916, was a quotient: a child's mental age from the Binet scale divided by their chronological age and multiplied by 100. That formula breaks down in adulthood, and David Wechsler replaced it in 1939 with the deviation score used by every modern test, which keeps the familiar centre of 100 but defines the units by the spread of scores in the norm sample rather than by age ratios. The page on how IQ is calculated walks through the arithmetic; this page explains what the number is.

What a modern IQ summarizes is performance across several kinds of task: verbal knowledge, fluid reasoning with novel material, quantitative reasoning, visual spatial ability, working memory and processing speed. Scores on those tasks correlate with one another, a fact Charles Spearman documented in 1904 and named the general factor, and the Full Scale score is the best single estimate of that common factor. In ACIS the Full Scale score is built from 20 subtests across six domains, has a composite reliability of .9886, a general factor loading of .958 and a standard error of 1.6 points, according to the technical manual, which means a reported 112 should be read as an interval of roughly 109 to 115 rather than as a point.

What the number predicts is well documented and moderate. Across longitudinal studies it correlates about 0.56 with educational attainment, 0.45 with occupational level and 0.23 with income; at the individual level it correlates about 0.81 with examination results five years later in a sample of 70,000 pupils; and in a whole birth cohort of Scots it predicts lower mortality from most major causes 68 years on. What it does not measure is also well documented: creativity, personality, emotional skill, wisdom and motivation are separate constructs with separate measures. The sections below take each part in turn, and the page on what IQ measures goes deeper into the content of the tasks.

1 From Binet to the Deviation Score: Where the Number Came From

The word quotient is a fossil, and the history of the number explains why the scale has a centre of 100, why the units are 15 points wide, and why an adult IQ is not a ratio of anything. In 1905 Alfred Binet and Théodore Simon published, in L'Année Psychologique, a scale of graded tasks for identifying schoolchildren in Paris who needed special instruction. The scale expressed a child's performance as a mental age, the age at which the average child passed the same items. In 1912 William Stern, in the work translated as The Psychological Methods of Testing Intelligence, proposed dividing mental age by chronological age so that a child of eight performing like a ten year old would have a quotient of 1.25; Lewis Terman's 1916 Stanford revision, The Measurement of Intelligence, multiplied the quotient by 100 and gave the world both the name and the round number.

The ratio worked well enough for children, whose mental ages rise steadily, and failed for adults, whose test performance stops rising in the late teens while their chronological age does not. A thirty year old performing like the average adult would, on the formula, have an IQ falling every year. David Wechsler, whose Measurement of Adult Intelligence accompanied the Wechsler Bellevue scale in 1939, replaced the quotient with a deviation score: a person's raw performance is compared with the distribution of performance among people of the same age in a norm sample, and expressed on a scale with a mean of 100 and a standard deviation of 15, chosen to resemble the range of the old ratio scores. Every modern test uses that convention, and the page on the history of IQ tells the longer story.

The change matters for reading a score. A ratio IQ of 150 in a child meant that the child was performing like children half again their age; a deviation IQ of 150 means that a person is 3.33 standard deviations above the mean of their age group, a position held by about one person in 2,300. The two numbers look the same and mean different things, which is why historical figures quoted for people tested before 1939, or estimated from biographies, cannot be placed on the modern scale, a point the page on mental age develops. An adult IQ today is a statement about rank within a norm sample, and nothing in it is a quotient.

2 What the Scale Is: Mean, Standard Deviation and Percentiles

The IQ scale is a normal distribution with its centre fixed at 100 and its spread fixed at 15 points, and every property of a score follows from those two numbers. In a normal distribution about 68 percent of people lie within one standard deviation of the mean, so about 68 percent of the reference population scores between 85 and 115; about 95 percent lie within two, between 70 and 130; and about 99.7 percent within three, between 55 and 145. The page on the standard deviation of 15 explains why 15 was chosen and what it does to the tails, and the page on score versus percentile shows the conversion: 100 is the 50th percentile, 110 about the 75th, 120 about the 91st, 130 about the 98th and 145 about the 99.9th. The percentile calculator performs the conversion for any score, and the rarity calculator turns it into one person in how many.

Not every test has used 15. The older Stanford-Binet editions used a standard deviation of 16, so that a 132 on those tests marked the same two standard deviations as a 130 on a Wechsler scale, and the Cattell scale used by some high IQ societies uses 24, so that 148 marks the same position. The page on the IQ score chart sets the scales side by side, and the rule for reading any score is to ask what standard deviation it was expressed on before comparing it with anything. ACIS uses 15, and its public classification bands are 90 to 109 Average, 110 to 119 High Average, 120 to 129 Superior, 130 to 134 Moderately Gifted, 135 to 144 Highly Gifted, 145 to 159 Exceptionally Gifted and 160 and above Profoundly Gifted, as the page on what IQ scores mean explains.

The scale has one more property that follows from the definition. Because 100 is the mean of the norm sample, the average IQ of the population a test was normed on is 100 by construction, at the time of norming, and it cannot be otherwise. A test normed in the United States in 2024 gives the average American of that year 100; a test normed in Britain in 2007 gives the average Briton of that year 100. The page on average IQ explains what follows for comparisons across countries and decades, and the page on IQ 100 takes the middle of the scale as its whole subject.

3 What an IQ Test Contains: Domains and the General Factor

A modern test is a battery of short tasks drawn from several cognitive domains, and an IQ is the summary of performance across them, weighted by how strongly each task reflects the ability they share. Spearman's 1904 observation was that children's marks in unrelated school subjects and their performance on simple sensory tasks were all positively correlated, and that a single common factor, which he called g, could account for much of the correlation. A century of factor analysis has refined the picture into a hierarchy: a general factor at the top, a set of broad abilities beneath it, and narrow abilities beneath those. The page on the g factor explains the statistics, and the page on the CHC model describes the Cattell Horn Carroll taxonomy that McGrew's 2009 account consolidated and that most current batteries, including ACIS, are built around.

The broad abilities that a Full Scale score summarizes are, in the language of the Wechsler scales and of ACIS, verbal comprehension, fluid reasoning, quantitative reasoning, visual spatial ability, working memory and processing speed. The page on the six cognitive domains describes each and the subtests that measure it; in ACIS, for example, Vocabulary asks for typed definitions, Matrix Reasoning asks which figure completes a pattern, Digit Span asks for sequences to be held and reordered, and Symbol Search asks for rapid visual decisions under a clock. Each subtest is scored on its own scale with a mean of 10 and a standard deviation of 3, the subtests in a domain combine into an index on the IQ scale, and the indices combine into the Full Scale score, as the page on Full Scale IQ sets out.

The weighting is not arbitrary. In the ACIS confirmatory factor analysis, a higher order general factor loads on the six domain indices at values from .648 for processing speed to .922 for fluid reasoning, and the Full Scale score built from all 20 subtests loads on the general factor at .958. That is the sense in which an IQ measures intelligence: it is the best available estimate of the factor that runs through all of the tasks, and the domain indices report the parts that are specific to each. A person is not their Full Scale score, and the profile of indices around it is usually the more informative part of a report, which is why the page on what IQ measures spends most of its length on the domains.

4 How an IQ Is Calculated

A score is produced in four steps, raw performance, scaled score, composite, and standard score, and the norm sample enters at the second step, which is why the sample defines the meaning of the number. On each subtest a person earns a raw score: items correct, points for the quality of definitions, or a count of correct decisions within the time limit. The raw score is then converted to a scaled score by looking up, in the norm table for the person's age band, where that raw performance falls in the reference distribution, and expressing it on a scale with a mean of 10 and a standard deviation of 3. The scaled scores in a domain are summed and converted, again by a norm table, to an index with a mean of 100 and a standard deviation of 15; the scaled scores of all core subtests are summed and converted to the Full Scale score in the same way. The page on how IQ scores are normed explains how the tables are built, and the page on how IQ is calculated works a full example.

The norm sample is therefore the whole meaning of the scale. A raw score of 40 on a vocabulary task is not high or low until it is placed against the distribution of raw scores among people of the same age in the reference group, and two tests with different reference groups can assign different IQs to the same raw performance. Publishers describe the sample in a technical manual: its size, age bands, sex ratio, education and, where relevant, region and language. ACIS describes an adult reference frame of 3,243 English speaking records aged 16 to 90, with a technical analysis set of 2,750 complete records used for the reliability and factor tables, and reports the age band distribution in the manual. That frame is what an ACIS score refers to, and the page on reliability and validity sets out what such a frame does and does not support.

Two consequences follow. The first is that scores are age relative: a sixty year old and a twenty year old with the same raw performance on a speeded task receive different scaled scores, because the norm tables for their age bands differ, and the page on whether IQ changes with age explains why. The second is that norms date. Raw performance has risen across the twentieth century, at about 2.31 points per decade in Trahan and colleagues' meta-analysis, so a norm table drawn in 1990 assigns higher IQs to people tested today than a table drawn in 2020 would, and the page on the Flynn effect explains the correction.

5 Reliability and Error: Why an IQ Is a Range

Every IQ carries a standard error, the expected size of the difference between the score a person obtained and the score they would obtain on average across many administrations, and a score read without its error is misread. The standard error of measurement is computed from the reliability of the score, using the relation that the error equals the standard deviation of the scale multiplied by the square root of one minus the reliability. For a Full Scale score with a reliability of .9886, as in ACIS, the error is 15 multiplied by the square root of 0.0114, which is 1.6 points, so a 95 percent confidence interval extends about three points either side of the reported score, by our arithmetic. For a domain index with a reliability of .92, the error is about 4.2 points and the interval about eight points wide. The technical manual reports the reliability and standard error of every ACIS index, and the page on reliability and validity explains how to read them.

The error is not the only source of instability. A second administration of the same test produces practice gains, because items and formats are familiar, and Wechsler manuals report retest gains of several points on Full Scale scores over short intervals. Conditions on the day, including sleep, anxiety and interruption, move scores by amounts the page on anxiety and IQ quantifies. And the norm sample itself is a sample, so that the tables carry sampling error beyond the measurement error of the individual. A published IQ should therefore be read as a band of perhaps five to ten points within which the true standing very probably lies, and differences between two people, or between two administrations, of less than that band should not be interpreted.

What reliability does support is the comparison of a person with a reference group and of a person's indices with one another, provided the differences exceed the error. A Verbal Comprehension Index of 118 and a Fluid Reasoning Index of 104 differ by 14 points, which is well beyond the combined error of the two indices and is a real feature of the profile; a difference of four points is not. The page on what IQ scores mean gives the rules of thumb, and a report that prints intervals beside its scores, as an ACIS report does, is the format that makes them usable.

6 What IQ Predicts, and How Much

An IQ predicts educational, occupational and health outcomes better than any other single psychological measurement, and the correlations are moderate, which means the number matters and does not determine anything. Strenze's meta-analysis of longitudinal studies in Intelligence in 2007 put the correlation between intelligence measured early in life and later educational attainment at 0.56, later occupational level at 0.45 and later income at 0.23, with intelligence predicting at least as well as parental socioeconomic status and school grades. Deary, Strand, Smith and Fernandes' study of more than 70,000 English pupils found a latent correlation of 0.81 between general ability at eleven and examination results at sixteen, the strongest relationship in the literature and the one the page on IQ and academic achievement examines.

For work, the figure most quoted for decades was Schmidt and Hunter's 0.51 for general mental ability and job performance, and Sackett, Zhang, Berry and Lievens' reanalysis in the Journal of Applied Psychology in 2022 revised it down to about 0.31 after correcting a systematic overcorrection for range restriction, which still leaves cognitive ability among the strongest predictors available to an employer. The page on IQ and job performance sets out the debate, and the page on IQ and income shows why the correlation with money is the weakest of the set. Gottfredson's Why g matters argued in 1997 that the predictive power comes from the complexity of everyday tasks, which the page on IQ and success discusses.

For health, Calvin and colleagues followed 65,765 Scots born in 1936 and tested at eleven in the Scottish Mental Survey of 1947 through 68 years of death records, and reported in the BMJ in 2017 that each standard deviation of higher childhood intelligence was associated with hazard ratios of 0.72 for respiratory disease, 0.75 for coronary heart disease, 0.76 for stroke, 0.82 for smoking related cancers and 0.84 for dementia, with only small attenuation after adjustment for childhood socioeconomic status. The page on IQ and longevity reviews the field of cognitive epidemiology that grew from those cohorts. The size of all of these correlations is the point to hold: a correlation of 0.5 leaves three quarters of the variance in the outcome to other things, and the number is a predictor among predictors.

7 Where Differences Come From: Genes, Environment and Schooling

Differences in IQ between people are partly heritable, partly environmental and partly the product of schooling, and the three facts sit together without contradiction once the meaning of each is clear. Plomin and Deary's five special findings in Molecular Psychiatry in 2015 summarize the genetic literature: the heritability of intelligence is substantial, it increases from childhood to adulthood, it is caused by many genes of very small effect, it is largely the same across different cognitive tests, and it overlaps with the heritability of educational attainment and health. Savage and colleagues' genome wide meta-analysis of 269,867 people in Nature Genetics in 2018 identified 205 genomic loci and 1,016 genes associated with intelligence, each of tiny effect and together explaining a small share of the variance. The page on what heritability actually means explains the concept, which is a population statistic and not a statement about any person or about the causes of group differences.

The environmental side is equally well established. Ritchie and Tucker-Drob's meta-analysis of quasi-experimental studies found that each additional year of education raises measured intelligence by about one to five points, persisting across the lifespan, and the page on reading and IQ reviews the twin evidence that reading ability contributes to later intelligence. The Flynn effect, documented in Flynn's 1987 paper on fourteen nations and quantified in the meta-analyses since, shows that raw performance in whole populations rose by roughly three points a decade through the twentieth century, which no genetic change could produce in that time. And the page on average IQ in India shows how nutrition, sanitation and schooling move test scores within a single country.

The reconciliation is that heritability describes the share of differences within a population under its current range of environments, and says nothing about how much a score can move when the environment changes. A trait can be highly heritable and highly responsive to schooling at once, and intelligence is both. The page on whether you can improve your IQ reviews what moves scores and what does not, and the list is short: education, reading, and the removal of the conditions that depress performance.

8 What IQ Does Not Measure

An IQ is a measure of cognitive ability as sampled by a battery of tasks, and the constructs it leaves out are as well defined as the ones it includes. The American Psychological Association's task force report, Neisser and colleagues' Intelligence: Knowns and Unknowns in 1996, set out the consensus: intelligence tests measure a range of cognitive abilities well, predict school and work outcomes moderately, and do not measure creativity, wisdom, practical sense, social skill or character, each of which contributes to a life. Gottfredson's Mainstream Science on Intelligence, signed by 52 researchers in 1997, made the same point from the other side: a high IQ is an advantage in life, and it is far from the only one.

Creativity correlates modestly with IQ and is measured separately, as the page on IQ and creativity explains. Personality traits are nearly independent of it, and the page on IQ and personality reviews the small correlations that exist. Emotional skill is a different construct with its own contested measures, which the page on emotional intelligence versus IQ examines, and wisdom, in the sense of judgment about what matters, is not on any test, as the page on intelligence versus wisdom discusses. The page on types of intelligence addresses the multiple intelligences proposals and why they have not displaced the general factor in measurement.

The practical consequence is that a score describes a person's standing on a defined set of abilities and nothing else. A person with a Full Scale IQ of 125 has reasoning and knowledge at about the 95th percentile of the reference frame; whether they are diligent, kind, original or wise is not in the number, and a reader who wants to know those things has to look elsewhere. The page on intelligence versus knowledge draws one more line that the number blurs, between what a person can work out and what they have learned, and the domain indices are the tool for separating them.

The omissions are not a flaw in the number; they are its definition. A measure that tried to include character, originality and judgment would lose the property that makes an IQ useful, which is that it estimates a defined set of abilities with a stated error and predicts a defined set of outcomes at a stated strength. Every other quality a reader cares about deserves its own measurement, and several have one.

9 Reading a Score: A Worked Example

A score is read in four moves, the scale, the norm group, the interval and the profile, and an illustrative ACIS report shows each of them. Suppose a report gives a Full Scale IQ of 112, an interval of 109 to 115, and domain indices of 121 for verbal comprehension, 106 for fluid reasoning, 110 for quantitative reasoning, 104 for visual spatial ability, 108 for working memory and 99 for processing speed; the numbers are illustrative and do not describe any person. The first move is the scale: ACIS reports on a mean of 100 and a standard deviation of 15, so 112 is 0.8 standard deviations above the mean. The second is the norm group: the reference frame is 3,243 English speaking adults aged 16 to 90, so 112 places the person at about the 79th percentile of that frame, in the High Average band of the public classification.

The third move is the interval. The Full Scale error of 1.6 points gives a 95 percent interval of about 109 to 115, so the person's true standing very probably lies between the 73rd and 84th percentiles, and a friend who scored 108 is not distinguishable from them on this evidence. The fourth move is the profile, which is where the report earns its length. The verbal index of 121 sits at about the 92nd percentile and exceeds the fluid index of 106 by 15 points, a difference well beyond the combined error of the two indices, so this is a person whose acquired knowledge and verbal reasoning run ahead of their reasoning with novel material, a pattern the page on fluid versus crystallized intelligence explains and that years of reading typically produce. The processing speed index of 99 is average, and the manual's guidance is to read a lower speed index beside the others rather than as a deficit, since speed tasks are the most sensitive to conditions on the day.

What the report does not say is as important. It does not say the person is a 112; it says the person performed, on this battery, on this occasion, at a level that places them in that band with that uncertainty. It does not say how they will perform on a different battery with a different norm sample, though the correlation between well constructed batteries is high. And it does not say anything about the qualities the previous section listed. The page on what a good IQ is answers the question most readers bring to a report, and the answer depends on what the score is for.

10 The Numbers That Are Not IQs

Several scores travel alongside an IQ and are confused with it, and a table is the quickest way to keep them apart. Each is a standard score or a rank, each has its own centre and spread, and none is convertible to another without knowing both.

The last row is the one most often mistaken for the first. A number produced by a quiz with no published norm sample, reliability or standard error is not an IQ in any sense this page has described, whatever scale it claims, and the page on free versus validated IQ tests explains how to tell the two apart. The page on the IQ percentile chart gives the full conversion between the standard scales.

11 Common Misreadings of the Number

Most confusion about IQ comes from reading a position as a quantity, a summary as a single ability, or a norm bound score as a universal one, and each misreading has a specific correction. The first is to treat an IQ as a fixed property of a person, like height. It is a measurement with error, it moves with conditions, and raw performance changes with schooling and with age; the page on common myths about IQ tests lists the variants. The second is to treat it as one ability. It is a summary of several, and two people with the same Full Scale score can have profiles that differ by twenty points in opposite directions on verbal and spatial indices; the profile is where the information is.

The third is to compare scores across tests and decades as if the scale were universal. A score refers to its norm sample, and the page on average IQ by country shows how far the tables of national IQs depend on that fact; the page on average IQ in the UK shows that the British mean is 100 because British samples define the scale. The fourth is to accept a number from a source without a norm sample. The page on whether online IQ tests are accurate sets out what a credible online battery publishes, and the page on the best online IQ tests ranks the ones that publish it.

The fifth misreading is the oldest: that a high score licenses a claim to genius, or a low one a verdict. The page on genius IQ traces the threshold to Terman's 1916 label and shows how little it was ever meant to carry, and the page on gifted IQ range describes what the upper bands do and do not predict. An IQ is a useful number precisely because its meaning is narrow, and the narrowness is the thing to keep.

A last misreading concerns the direction of the arithmetic. Because the scale is anchored to a norm sample, a person's IQ can change without the person changing at all: a new edition with fresh norms, or a different battery with a different reference group, assigns a different number to the same performance, and the difference is a property of the tables. The honest reading of any two numbers is therefore a reading of two norm samples first, and a reader who holds that rule will find that most apparent contradictions between scores, between tests and between decades dissolve into it.

12 Sources Behind This Page

Every figure above is traceable to one of the following, and each is linked at the point where it is used. ACIS reliability, loading and standard error figures are from the technical manual, version 1.4; the conversion of reliability to standard error and of scores to percentiles is our arithmetic and is labelled as such where it appears.

• Binet A and Simon T. New methods for the diagnosis of the intellectual level of subnormals. L'Année Psychologique, 1905, volume 12, pages 191 to 244, in the translation by Elizabeth Kite. psychclassics.yorku.ca.
• Stern W. The Psychological Methods of Testing Intelligence. Warwick and York, 1914, translated by Guy Montrose Whipple. archive.org.
• Terman L M. The Measurement of Intelligence. Houghton Mifflin, 1916. archive.org.
• Wechsler D. The Measurement of Adult Intelligence. Williams and Wilkins, 1939. archive.org.
• Spearman C. "General intelligence," objectively determined and measured. The American Journal of Psychology, 1904, volume 15, issue 2, pages 201 to 292.
• McGrew K S. CHC theory and the human cognitive abilities project: Standing on the shoulders of the giants of psychometric intelligence research. Intelligence, 2009, volume 37, issue 1, pages 1 to 10.
• Neisser U, Boodoo G, Bouchard T J, Boykin A W, Brody N, Ceci S J, Halpern D F, Loehlin J C, Perloff R, Sternberg R J and Urbina S. Intelligence: Knowns and unknowns. American Psychologist, 1996, volume 51, issue 2, pages 77 to 101.
• Gottfredson L S. Mainstream science on intelligence: An editorial with 52 signatories, history, and bibliography. Intelligence, 1997, volume 24, issue 1, pages 13 to 23.
• Gottfredson L S. Why g matters: The complexity of everyday life. Intelligence, 1997, volume 24, issue 1, pages 79 to 132.
• Strenze T. Intelligence and socioeconomic success: A meta-analytic review of longitudinal research. Intelligence, 2007, volume 35, issue 5, pages 401 to 426.
• Deary I J, Strand S, Smith P and Fernandes C. Intelligence and educational achievement. Intelligence, 2007, volume 35, issue 1, pages 13 to 21.
• Sackett P R, Zhang C, Berry C M and Lievens F. Revisiting meta-analytic estimates of validity in personnel selection: Addressing systematic overcorrection for restriction of range. Journal of Applied Psychology, 2022, volume 107, issue 11, pages 2040 to 2068.
• Calvin C M, Batty G D, Der G, Brett C E, Taylor A, Pattie A, Čukić I and Deary I J. Childhood intelligence in relation to major causes of death in 68 year follow-up: prospective population study. BMJ, 2017, volume 357, article j2708.
• Plomin R and Deary I J. Genetics and intelligence differences: five special findings. Molecular Psychiatry, 2015, volume 20, issue 1, pages 98 to 108.
• Ritchie S J and Tucker-Drob E M. How much does education improve intelligence? A meta-analysis. Psychological Science, 2018, volume 29, issue 8, pages 1358 to 1369.
• Trahan L H, Stuebing K K, Fletcher J M and Hiscock M. The Flynn effect: A meta-analysis. Psychological Bulletin, 2014, volume 140, issue 5, pages 1332 to 1360.

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