Top 40%
What IQ is the top 40 percent?
The 60th percentile on the bell curve, on three common scales, with what a score at that line means.
Short answer
The top 40% of IQ scores starts at about 104 on the standard scale (mean 100, standard deviation 15); the exact cut is 103.8. That is the 60th percentile, about 1 in 3 people. On a scale with standard deviation 16 the cut is about 104, and on the SD 24 Cattell scale about 106.
Specimen · Top 40%
40%Top
- Cut at
- IQ 103.8
- Classification
- Average
- z-score
- +0.25
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| Scale | IQ at the 60th percentile |
|---|---|
| Standard deviation 15 (Wechsler, SB5) | 103.8 |
| Standard deviation 16 (older Stanford-Binet) | 104.1 |
| Standard deviation 24 (Cattell Culture Fair III) | 106.1 |
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 40% of the curve above it, multiply by the scale's standard deviation and add 100. For the 60th percentile the z score is 0.253, so the cut is 103.8 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 104.1 and 106.1 there. The percentile to IQ converter does this for any percentile.
What a score at the top 40% line means
A score of 104 is labeled Average on the WAIS-IV scale (Wikipedia: IQ classification). It is inside the 85 to 115 range where about 68% of people score (the 68-95-99.7 rule), so the top 40% is above the middle but still part of the typical range.
In a group of 30 people the same age, about 12 would be expected to score at or above 104. Percentiles near the middle of the curve are close together in points: a few IQ points can move you several percentiles, while out in the tails the same few points barely move the percentile at all.
A percentile is not a percentage of questions
The 60th percentile means scoring higher than 60% 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 104 |
|---|---|---|
| Top 30% | 107.9 | +4.1 |
| Median | 100.0 | -3.8 |
See the score itself on IQ 104, 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