What is IQ?
Intelligence Quotient (IQ) is a standardized score designed to assess human cognitive abilities relative to the general population. The concept was first introduced by German psychologist William Stern in 1912, who proposed dividing a person's mental age (as measured by the Binet-Simon test) by their chronological age and multiplying by 100. While the original ratio IQ has been replaced by the deviation IQ, the term persists.
Modern IQ tests, including the Wechsler Adult Intelligence Scale (WAIS), Stanford-Binet Intelligence Scales, and Raven's Progressive Matrices, use deviation IQ scoring. In this system, scores are normed so that the mean of the general population is 100 and the standard deviation is 15. This means approximately 68% of people score between 85 and 115, about 95% score between 70 and 130, and roughly 99.7% score between 55 and 145.
IQ tests typically measure multiple cognitive domains, including verbal comprehension, perceptual reasoning, working memory, and processing speed. The full-scale IQ (FSIQ) represents a composite of these domain scores and is the number most commonly reported. Individual domain scores can vary significantly within the same person, a phenomenon known as score scatter, which is why a single IQ number provides only a partial picture of cognitive abilities.
The Bell Curve
IQ scores follow a normal (Gaussian) distribution, also known as a bell curve. This distribution is defined by two parameters: the mean (average) and the standard deviation (a measure of spread). For IQ, the mean is fixed at 100 and the standard deviation at 15 points. The mathematical properties of the normal distribution allow us to calculate the exact percentage of the population that falls above or below any given IQ score.
The bell curve is symmetric around the mean, meaning that the same proportion of people fall equally far above the mean as below it. For example, about 2.3% of the population has an IQ below 70, and the same 2.3% has an IQ above 130. The curve is steepest near the mean and flattens out toward the tails, reflecting the fact that extreme scores (both high and low) are increasingly rare.
The conversion from IQ to percentile uses the cumulative distribution function (CDF) of the normal distribution. The z-score is first calculated as (IQ - 100) / 15, and then the CDF at that z-score gives the proportion of the population that scores at or below that IQ. This proportion, multiplied by 100, is the percentile rank.
Percentile Meaning
A percentile rank indicates the percentage of the population that scores at or below a given value. An IQ at the 84th percentile means the person scored higher than 84% of the population and lower than 16%. The 50th percentile corresponds to an IQ of exactly 100 (the population mean).
Percentiles are often more intuitive than raw IQ scores for understanding relative standing. The difference between percentiles is not uniform: moving from the 50th to the 60th percentile requires a smaller IQ increase (about 4 points) than moving from the 90th to the 95th percentile (about 5 points) or from the 95th to the 99th percentile (about 10 points). This reflects the compression of the bell curve at the extremes, where each additional IQ point represents a larger jump in percentile rank among the relatively few people who score at that level.
In educational and clinical settings, percentile ranks are commonly used alongside IQ scores because they are easier for non-specialists to interpret. Telling a parent that their child scored at the 91st percentile (meaning better than 91% of same-age peers) is often more meaningful than stating an IQ of 120.
IQ Classification Table
| IQ Range | Classification | Percentile | Rarity |
|---|---|---|---|
| < 70 | Very Low | < 2.3rd | 1 in 44 |
| 70 – 84 | Below Average | 2.3rd – 16th | 1 in 6 |
| 85 – 114 | Average | 16th – 84th | 1 in 1.5 |
| 115 – 129 | Above Average | 84th – 97.7th | 1 in 6 |
| 130 – 144 | Gifted | 97.7th – 99.87th | 1 in 44 |
| 145 – 159 | Genius / Exceptional | 99.87th – 99.997th | 1 in 741 |
| 160+ | Extraordinary Genius | > 99.997th | 1 in 31,560 |
These classifications are approximate and vary slightly between different IQ test publishers. The Wechsler scales, for instance, use somewhat different descriptive labels than the Stanford-Binet. The boundaries between categories are not rigid clinical thresholds but rather convenient reference points for communication.
IQ Distribution Diagram
Notable IQ Scores
While reported IQ scores of historical and contemporary figures should be taken with caution (many are estimates rather than verified test results), they provide an interesting reference point for understanding the scale:
- Albert Einstein: Estimated at 160, though he was never formally tested with a modern IQ assessment. His extraordinary contributions to physics are well documented regardless of any numerical score.
- Stephen Hawking: Often cited at around 160, though Hawking himself reportedly said, "People who boast about their IQ are losers." His work on black holes and cosmology speaks for itself.
- Marilyn vos Savant: Recorded a score of 228 on the Stanford-Binet (L-M) at age 10, though this ratio IQ does not directly compare to modern deviation IQ scores. She was listed in the Guinness Book of World Records for highest recorded IQ.
- Terence Tao: Scored 220-230 on ratio-based tests as a child. The mathematician has made groundbreaking contributions to number theory, harmonic analysis, and partial differential equations.
It is important to note that IQ tests have practical ceilings. Most standardized tests are normed only to about IQ 160, and scores above this level become increasingly unreliable and difficult to interpret. The extreme scores sometimes reported for historical figures are often extrapolations or based on older, less standardized testing methods.
Limitations of IQ Testing
Despite their widespread use, IQ tests have significant limitations that should be understood when interpreting results:
- Cultural bias: IQ tests were developed within specific cultural contexts and may disadvantage individuals from different cultural backgrounds. Questions about vocabulary, general knowledge, and even visual patterns can reflect cultural exposure rather than innate cognitive ability.
- Narrow definition of intelligence: IQ tests primarily measure analytical and logical reasoning abilities. They do not adequately capture creative intelligence, emotional intelligence, practical intelligence, musical ability, kinesthetic intelligence, or social skills, all of which are important for real-world success.
- Test conditions matter: Anxiety, fatigue, motivation, test-taking experience, and rapport with the examiner can all significantly affect scores. A person's IQ score on any given day may vary by 5 to 10 points or more due to these factors.
- Practice effects: Repeated testing with the same or similar IQ tests can lead to score increases of 5 to 15 points, reflecting familiarity with the test format rather than actual cognitive improvement.
- Not a measure of worth: IQ scores do not determine a person's value, potential for happiness, moral character, or ultimate success in life. Many highly successful and fulfilled individuals have average IQ scores, while some with very high IQ scores struggle with mental health, relationships, or practical life skills.
- Flynn Effect: Average IQ scores have been rising by about 3 points per decade across populations, suggesting that the tests measure something that is responsive to environmental changes (education, nutrition, test familiarity) rather than a fixed biological trait.
Worked Example
For an IQ score of 115:
This means a person with an IQ of 115 scored higher than approximately 84.1% of the general population. The classification is Above Average, and the rarity is approximately 1 in 6 people (about 15.9% of the population scores 115 or higher). The z-score of 1.00 indicates this IQ is exactly one standard deviation above the mean.
Frequently Asked Questions
What IQ score is considered genius?
There is no universally agreed-upon IQ threshold for "genius." Most classification systems place the "gifted" category at IQ 130 and above (the top 2.3% of the population). Some systems reserve "genius" or "exceptional" for IQ 145 and above (the top 0.13%). However, genius in the everyday sense refers to extraordinary creative or intellectual achievement, which does not correlate perfectly with IQ scores.
Can IQ change over time?
IQ scores are relatively stable in adulthood but are not perfectly fixed. Childhood IQ scores can fluctuate significantly as the brain develops, and environmental factors like education, nutrition, and enrichment can influence scores. In adulthood, IQ tends to remain fairly stable until advanced age, when some cognitive abilities (particularly processing speed) may decline while others (like vocabulary) remain stable or even improve.
What is the average IQ?
By definition, the average IQ is 100 (the 50th percentile). About 68% of the population scores between 85 and 115, which is considered the average range. IQ tests are periodically re-normed to maintain this average of 100, which is how the Flynn Effect (rising raw scores over time) is accounted for in the scoring system.
Is IQ the same as intelligence?
No. IQ tests measure specific cognitive abilities, primarily analytical reasoning, pattern recognition, processing speed, and memory. Intelligence is a much broader concept that includes creativity, emotional understanding, practical problem-solving, adaptability, and wisdom, none of which are fully captured by a standard IQ test. IQ correlates with certain life outcomes (academic performance, some job categories) but is far from a complete measure of mental capability.
What is the difference between Wechsler and Stanford-Binet scales?
Both use a mean of 100 and standard deviation of 15. The Wechsler scales (WAIS for adults, WISC for children) are the most commonly administered and provide composite scores for verbal comprehension, perceptual reasoning, working memory, and processing speed. The Stanford-Binet (5th Edition) uses a similar structure with five factor indices. Both are considered valid and reliable measures, and scores between the two are generally comparable, though individual results may differ by a few points.
Does a high IQ guarantee success?
No. While higher IQ scores correlate with better academic performance and higher income on average, the relationship is far from deterministic. Factors like motivation, persistence, emotional regulation, social skills, opportunity, physical health, and sheer luck all play significant roles in determining life outcomes. Beyond an IQ of about 120, additional IQ points have diminishing returns for predicting real-world success.