<p>Most &quot;professional&quot; IQ tests are capped at around 160 points (<a href="https://www.theguardian.com/society/2015/sep/02/girl-12-wins-maximum-mensa-iq-test-score" rel="nofollow noreferrer">Mensa</a>: 162, <a href="https://en.wikipedia.org/wiki/Stanford%E2%80%93Binet_Intelligence_Scales" rel="nofollow noreferrer">Stanford Binet</a>: 160, <a href="https://www.sciencedirect.com/topics/medicine-and-dentistry/wechsler-intelligence-scale" rel="nofollow noreferrer">WAIS-IV</a>: 160), so scores above 200 are not relevant in analysis using data from those.</p>
<p>There's also a logical flaw in your claim that an IQ above 195 <em>should not</em> be measurable &quot;statistically&quot;: even if it's extremely unlikely, it's <em>possible</em> by the definition of a continuous normal distribution.</p>
<p>Score outliers above 195 are typically measured by non-standard IQ tests or subjectively evaluated. They should not be considered as data points in the context of statistical analysis.</p>

CC BY-SA 4.0
2022-12-05T20:46:37.177Z
2022-12-05T22:37:08.140Z
2022-12-05T22:37:08.140Z
belkarx
<p>Your math appears to be correct. If one understands the relation between reliability and validity, one understands that an IQ upwards of 160 would be practically impossible to measure. This is because validity is limited by reliability. We cannot create a measure of IQ that could identify someone over 160 because we can't locate enough people to reliably create such a test. We cannot obtain a normative sample of a large enough size to get a handful of people with an IQ of 175, 5 SDs above the mean. Just remember, a measure can't be valid if it isn't reliable.</p>

CC BY-SA 4.0
2022-12-05T08:25:49.203Z
Please add sources to your claims.
AliceD
CC BY-SA 4.0
2022-12-04T06:41:30.400Z
2022-12-04T06:41:30.400Z
Ethan Lantz
<p>IQ scores are supposedly put on a normal distribution with a standard deviation of 15.</p>
<p>The population of the world is about 7,674,000,000.</p>
<p>So, if I know my statistics and made no numerical errors, the smartest person in the world (even given the unrealistic assumption that we could measure everybody's intelligence), would only have an IQ of 194.8083.</p>
<p><a href="https://i.sstatic.net/NHHTY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NHHTY.png" alt="screenshot from Wolfram Alpha" /></a></p>
<p>Double the population of the world and the max measurable IQ only goes to 196.4.</p>
<p>Given this, why do I see occasional reports of measured IQs above 200?  A 200 IQ, statistically, would require a population of at least 76 billion people, ten times more than there are humans now. A 220 IQ would require 10,000 times as many people as that.</p>
<p>Does the math and statistics just get ignored for those high scores, or is the scale different somehow?</p>

CC BY-SA 4.0
2021-06-22T19:57:00.783Z
Similar to: [Why does IQ have a truncated normal distribution?](https://psychology.stackexchange.com/q/25089/7001), [IQ scores - fixed raw scores vs infinite tails of the underlying normal distribution of standard scores](https://psychology.stackexchange.com/q/16284/7001).  Also see the answer to: [How to calculate IQ score based on raw score and adjust for age?](https://psychology.stackexchange.com/q/4483/7001).
Arnon Weinberg
CC BY-SA 4.0
2022-05-30T10:42:08.757Z
It heavily depends on the "occasional reports". While this world has only 7b-ish people, we could still reasonably generate a distribution that predicts a theoretical IQ assignment on a larger scale, with many statistic tricks, with defined condition and confidence. That said, 10/11 these reports are scientifically BS (below standard).
X Zhang
<statistics><iq>
Are IQ scores above 200 statistically meaningful?
onigame
# Are IQ scores above 200 statistically meaningful?

(Asked by: username_0 on 2021-06-22)

IQ scores are supposedly put on a normal distribution with a standard deviation of 15.

The population of the world is about 7,674,000,000.

So, if I know my statistics and made no numerical errors, the smartest person in the world (even given the unrealistic assumption that we could measure everybody's intelligence), would only have an IQ of 194.8083.

[![screenshot from Wolfram Alpha](https://i.sstatic.net/NHHTY.png)](https://i.sstatic.net/NHHTY.png)

Double the population of the world and the max measurable IQ only goes to 196.4.

Given this, why do I see occasional reports of measured IQs above 200? A 200 IQ, statistically, would require a population of at least 76 billion people, ten times more than there are humans now. A 220 IQ would require 10,000 times as many people as that.

Does the math and statistics just get ignored for those high scores, or is the scale different somehow?

**Tags:** statistics, iq

> **Comments:**
> **username_1**: Similar to: [Why does IQ have a truncated normal distribution?](https://psychology.stackexchange.com/q/25089/7001), [IQ scores - fixed raw scores vs infinite tails of the underlying normal distribution of standard scores](https://psychology.stackexchange.com/q/16284/7001).  Also see the answer to: [How to calculate IQ score based on raw score and adjust for age?](https://psychology.stackexchange.com/q/4483/7001).  
> **username_2**: It heavily depends on the "occasional reports". While this world has only 7b-ish people, we could still reasonably generate a distribution that predicts a theoretical IQ assignment on a larger scale, with many statistic tricks, with defined condition and confidence. That said, 10/11 these reports are scientifically BS (below standard).  

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## 2 answers

### Answer by username_3 on 2022-12-05. Score: 2

Most "professional" IQ tests are capped at around 160 points ([Mensa](https://www.theguardian.com/society/2015/sep/02/girl-12-wins-maximum-mensa-iq-test-score): 162, [Stanford Binet](https://en.wikipedia.org/wiki/Stanford%E2%80%93Binet_Intelligence_Scales): 160, [WAIS-IV](https://www.sciencedirect.com/topics/medicine-and-dentistry/wechsler-intelligence-scale): 160), so scores above 200 are not relevant in analysis using data from those.

There's also a logical flaw in your claim that an IQ above 195 *should not* be measurable "statistically": even if it's extremely unlikely, it's *possible* by the definition of a continuous normal distribution.

Score outliers above 195 are typically measured by non-standard IQ tests or subjectively evaluated. They should not be considered as data points in the context of statistical analysis.


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### Answer by username_4 on 2022-12-04. Score: 0

Your math appears to be correct. If one understands the relation between reliability and validity, one understands that an IQ upwards of 160 would be practically impossible to measure. This is because validity is limited by reliability. We cannot create a measure of IQ that could identify someone over 160 because we can't locate enough people to reliably create such a test. We cannot obtain a normative sample of a large enough size to get a handful of people with an IQ of 175, 5 SDs above the mean. Just remember, a measure can't be valid if it isn't reliable.

> **Comments:**
> **username_5**: Please add sources to your claims.  

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