How performance on many cognitive tasks becomes a standardized number, what 100 and 115 mean, and what an IQ score can and cannot tell us.
IQ is a standardized score designed to estimate a person’s cognitive ability relative to an appropriate normative population.
Modern IQ is not calculated as “mental age divided by chronological age.” That historical formula is no longer how major contemporary intelligence tests produce adult IQ scores.
Instead, a person completes a standardized set of cognitive tasks. Their performance is scored according to the test’s rules, converted using an appropriate normative reference distribution—commonly age-specific norms—and combined into one or more standardized composite scores.
A worked example: from answers to an IQ score
The example below is deliberately fictional and does not reproduce any protected test items, scoring rules or proprietary norms.
Imagine Maya, age 30, completes a cognitive battery with tasks sampling verbal knowledge, abstract reasoning, visual-spatial reasoning, working-memory-related performance and processing speed.
Step 1: raw performance
On each task, Maya produces raw responses: correct answers, errors, items completed or another task-specific performance measure.
A raw score by itself is usually hard to interpret. Forty correct answers might be outstanding on one task and ordinary on another.
Step 2: compare with the normative group
The test publisher has previously administered the battery under standardized conditions to a carefully constructed sample. Maya’s raw scores are converted using age-appropriate normative tables or reference distributions into scores showing how her performance compares with the relevant age group.
This comparison is what gives the numbers meaning.
Step 3: combine information
Scores from multiple tasks may be combined into broad indices and an overall composite according to the instrument’s validated scoring model.
A fictional summary might look like this:
| Broad area | Illustrative standardized result |
|---|---|
| Verbal knowledge | 112 |
| Fluid reasoning | 118 |
| Visual-spatial | 109 |
| Working-memory-related | 104 |
| Processing speed | 101 |
| Full-scale composite | 111 |
These are illustrative only. Actual instruments differ in what they measure and how they combine scores.
Step 4: interpret the scale
On many widely used contemporary IQ scales, 100 is set as the normative mean and 15 points as one standard deviation.
That means:
- IQ 100 is at the mean of the reference distribution;
- IQ 115 is one standard deviation above the mean;
- IQ 85 is one standard deviation below;
- IQ 130 is two standard deviations above.
An IQ of 115 does not mean “15 percent more intelligent” than an IQ of 100. The scale is not a ratio scale with a meaningful zero point. The difference represents position on a standardized distribution.
Why is 100 the average?
Because the score scale is constructed that way during norming.
Psychologists could express the same relative performance using z-scores, T-scores, percentiles or other transformations. IQ’s mean of 100 is a convention chosen for interpretability.
The important scientific information is not the magical significance of the number 100. It is where performance falls relative to the normative distribution and how much uncertainty surrounds that estimate.
So is IQ measuring g?
Usually, a broad full-scale IQ is intended to estimate general cognitive ability and often correlates strongly with psychometric g. But IQ and g are not identical.
g is estimated from the covariance among cognitive measures. IQ is a score generated by a specific standardized instrument.
A full-scale IQ reflects much of the same general variance, but it also depends on which tasks the test includes, how those tasks are weighted and combined, and measurement error. Some batteries also report broad index scores that contain domain-specific information beyond the overall composite.
A useful shorthand is:
g = the common latent dimension
IQ = a standardized measurement result designed to estimate broad cognitive ability
How precise is 111?
Not perfectly precise. Every IQ score has measurement error.
If Maya receives a Full Scale IQ of 111, responsible interpretation does not treat 111 as an exact reading of her permanent cognitive capacity. Tests report reliability information and can provide a confidence interval around the obtained score.
The precise interval depends on the instrument, age and score. The important principle is that the observed number is an estimate.
This matters near cutoffs. A person scoring 69 and a person scoring 71 are not separated by a natural psychological cliff merely because an administrative system uses 70 as one criterion. Measurement uncertainty and other diagnostic information matter.
What does percentile mean?
Percentiles answer a different question from IQ points.
A percentile describes the proportion of the normative distribution at or below a score. Because IQ scores are approximately normally distributed by construction in many norming systems, one standard deviation above the mean corresponds roughly to the 84th percentile, while two standard deviations above corresponds roughly to the 98th percentile.
The relationship between IQ points and percentiles is nonlinear. Moving from 100 to 115 changes percentile position much more than a casual reading of “15 points” suggests.
Does IQ measure all of intelligence?
No test samples everything a person can do.
Professional intelligence batteries usually sample several well-established cognitive domains. They are designed to provide reliable evidence about broad cognitive ability, not to measure every human strength.
Creativity, wisdom, personality, motivation, moral judgment, practical expertise and social knowledge are not simply omitted subtests of one giant IQ construct.
But the opposite claim—“IQ only measures how good you are at IQ tests”—also goes too far. Intelligence-test scores show substantial relationships with learning and other external outcomes. Their validity is precisely why they are scientifically useful.
Can someone prepare for an IQ test?
Familiarity, practice and coaching can affect performance on particular tasks, especially when a person encounters similar material repeatedly. That is one reason standardized administration and appropriate retest intervals matter.
But becoming better at a practiced item type does not automatically demonstrate a broad increase in general cognitive ability. The scientific question is transfer: does improvement generalize to sufficiently different measures and persist over time?
IQ is a norm-referenced estimate, not a percentage of intelligence and not a direct measurement of a physical quantity.
The number becomes meaningful because a standardized procedure compares performance with a reference population. Broad IQ composites are useful partly because they aggregate information across several tasks, but every score contains uncertainty and represents only the constructs sampled by the instrument.
References
- American Educational Research Association, American Psychological Association, & National Council on Measurement in Education. (2014). Standards for Educational and Psychological Testing. DOI
- McMillen, P., & Levin, M. (2024). Collective intelligence: A unifying concept for integrating biology across scales and substrates. Communications Biology, 7, 378. DOI
- Schneider, W. J., & McGrew, K. S. (2018). The Cattell-Horn-Carroll theory of cognitive abilities. In Contemporary Intellectual Assessment.
- McGrew, K. S. (2009). CHC theory and the human cognitive abilities project. Intelligence, 37, 1–10. —
