50th percentile
What is the median IQ?
The median and the mean are the same number on the IQ scale. Here is why, and what the middle of the curve looks like.
Short answer
The median IQ is 100. On every properly normed IQ test, scores are standardized so the middle of each age group lands on 100, whatever the standard deviation of the scale. Half of people score above 100 and half below. The WAIS-IV labels 90 to 109 Average.
Specimen · 50th percentile
50th
- Cut at
- IQ 100.0
- Classification
- Average
- z-score
- 0.00
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| Scale | IQ at the 50th percentile |
|---|---|
| Standard deviation 15 (Wechsler, SB5) | 100.0 |
| Standard deviation 16 (older Stanford-Binet) | 100.0 |
| Standard deviation 24 (Cattell Culture Fair III) | 100.0 |
How the cut is calculated
IQ scores are standardized to a normal curve with mean 100 (Wikipedia: Intelligence quotient). To find the score at a percentile, take the z score that leaves half the curve below it, multiply by the scale's standard deviation and add 100. For the 50th percentile the z score is 0.000, so the cut is 100.0 on SD 15. Older Stanford-Binet forms used SD 16 and the Cattell Culture Fair III scale uses SD 24 (Wikipedia: IQ classification), which is why the same percentile reads as 100.0 and 100.0 there. The percentile to IQ converter does this for any percentile.
Why the middle is exactly 100
Modern IQ tests are standardized so that each age group has a mean of 100 (Wikipedia: Intelligence quotient). Because the scores follow a symmetric bell curve, the mean and the median coincide: the middle person in a line of everyone your age scores 100. That is true on the SD 15, 16 and 24 scales alike, because rescaling stretches the curve around 100 without moving it.
The middle is also crowded. About 68% of people score between 85 and 115 (the 68-95-99.7 rule), and the WAIS-IV Average band, 90 to 109, holds about half of everyone (Wikipedia: IQ classification). A few points either side of 100 barely moves the percentile: 95 is about the 36.9 percentile and 105 about the 63.1.
A percentile is not a percentage of questions
The 50th percentile means scoring higher than 50% of people the same age, not answering that share of questions correctly. See whether an IQ score is a percentage for the difference.
Neighboring percentiles
| Percentile | IQ (SD 15) | Gap from 100 |
|---|---|---|
| Top 40% | 103.8 | +3.8 |
| Bottom 25% | 89.9 | -10.1 |
See the score itself on IQ 100, every cut on the IQ by percentile page, or any score on the IQ score chart.
Sources
- Intelligence quotient. Wikipedia. en.wikipedia.org/wiki/Intelligence_quotient
- IQ classification. Wikipedia. en.wikipedia.org/wiki/IQ_classification
- 68-95-99.7 rule. Wikipedia. en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule