Bottom 2%
What IQ is the bottom 2 percent?
The 2nd 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 2% of IQ scores is about 69 and below on the standard scale (mean 100, standard deviation 15); the exact cut is 69.2. That is the 2nd percentile, about 1 in 50 people. On a scale with standard deviation 16 the cut is about 67, and on the SD 24 scale about 51.
Specimen · Bottom 2%
2%Bottom
- Cut at
- IQ 69.2
- Classification
- Extremely Low
- z-score
- −2.05
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| Scale | IQ at the 2nd percentile |
|---|---|
| Standard deviation 15 (Wechsler, SB5) | 69.2 |
| Standard deviation 16 (older Stanford-Binet) | 67.1 |
| Standard deviation 24 (Cattell Culture Fair III) | 50.7 |
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 2% of the curve below it, multiply by the scale's standard deviation and add 100. For the 2nd percentile the z score is -2.054, so the cut is 69.2 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 67.1 and 50.7 there. The percentile to IQ converter does this for any percentile.
What a score in the bottom 2% means
A score of 69 is labeled Extremely Low 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 69 is consistent with a true score from 64 to 74, about the 0.82 to 4.2 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 2nd percentile means scoring higher than 2% 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 69 |
|---|---|---|
| Bottom 5% | 75.3 | +6.1 |
| Bottom 1% | 65.1 | -4.1 |
See the score itself on IQ 69, 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.