Bottom 20%
What IQ is the bottom 20 percent?
The 20th percentile on the bell curve, on three common scales, with what a score in that range does and does not mean.
Short answer
The bottom 20% of IQ scores is about 87 and below on the standard scale (mean 100, standard deviation 15); the exact cut is 87.4. That is the 20th percentile, about 1 in 5 people. On a scale with standard deviation 16 the cut is about 87, and on the SD 24 scale about 80.
Specimen · Bottom 20%
20%Bottom
- Cut at
- IQ 87.4
- Classification
- Low Average
- z-score
- −0.84
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| Scale | IQ at the 20th percentile |
|---|---|
| Standard deviation 15 (Wechsler, SB5) | 87.4 |
| Standard deviation 16 (older Stanford-Binet) | 86.5 |
| Standard deviation 24 (Cattell Culture Fair III) | 79.8 |
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 20% of the curve below it, multiply by the scale's standard deviation and add 100. For the 20th percentile the z score is -0.842, so the cut is 87.4 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 86.5 and 79.8 there. The percentile to IQ converter does this for any percentile.
What a score in the bottom 20% means
A score of 87 is labeled Low Average on the WAIS-IV scale (Wikipedia: IQ classification). Labels describe score ranges on one test; they are not diagnoses. A low score on any single session can reflect tiredness, an unfamiliar format, distraction or a small screen as much as ability.
Clinical scores carry measurement error of around plus or minus 5 points at 95% (Wechsler, 2008), so a measured 87 is consistent with a true score from 82 to 92, about the 11.5 to 29.7 percentile. Questions about a learning or intellectual disability need a full assessment by a licensed psychologist, not an online estimate.
A percentile is not a percentage of questions
The 20th percentile means scoring higher than 20% 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 87 |
|---|---|---|
| Bottom 25% | 89.9 | +2.5 |
| Bottom 10% | 80.8 | -6.6 |
See the score itself on IQ 87, 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
- Wechsler, D. (2008). WAIS-IV Technical and Interpretive Manual. Pearson.