I am a lay person and new to this, and while I do understand that 145 IQ means 3 SDs up from the mean, I want to have a rough idea of what it means in real-life examples, from people who have experience in this domain. What is it that a person with a 145 IQ can typically do that a persona with a 100 IQ can typically not do? Examples of feats or the like is appreciated.
1$\begingroup$ The answer about three standard deviations is correct. But you cannot state that someone is 45% smarter. Makes no sense. Nominal, ordinal, interval and ratio are the types of scales used, and IQ is an interval scale with no zero point (an IQ of zero does not mean no intelligence like zero pounds of flour means none). Ask a mathematician why it takes a true zero point for that. $\endgroup$– william f wallaceJun 7, 2017 at 0:02
2$\begingroup$ I don't think it is correct to use "intelligence" and "IQ" as synonyms. IQ tests measure IQ, that is, they measure the thing that they measure. "Intelligence" is undefined or has many definitions, and has many dimensions. $\endgroup$– amacaJun 8, 2017 at 9:14
$\begingroup$ I can't find the source I read it from, hence this isn't an actual answer, but I remember reading somewhere that the further up the IQ scores you go, the more reliant on speed it is and the less reliant on difficulty. Once you've got all the questions in your test right, you're arguably no more clever than anyone else who also got all the questions right within a reasonable timescale. The subtle difference in the speed at which you arrive at a sound solution is a different metric to the ratio of sound to unsound solutions you arrive at. $\endgroup$– IsaacsonJun 8, 2017 at 10:07
As a general note, precision in measurement of intelligence declines as you move to more extreme levels. There is greater uncertainty in measurement in the 145 range than there is at the 100 range. Norm samples get smaller, and most measures of intelligence are designed for the normal range.
Categories: You might find the article on IQ classification useful. The article discusses a wide range of ways to give verbal labels to IQ scores. For example, the following categories would put a 145 IQ person above "very superior" intelligence.
Statistical interpretations: You correctly note that 145 represents 3 standard deviations above the mean. If you assume a normal distribution and no measurement error, IQ 100 means you are more intelligent than 50% of the population, and an IQ of 145 means you are more intelligent than 99.9% of the population. Or to put another way, 1 in 2 people have an IQ greater than 100, and roughly 1 in 750 people have an IQ of greater than 145.
Intuition: If you went to a large representative high school (say with 500 to 1000 students), you might think of the typical student as your 100 IQ student, and the smartest kid in school as possibly being in the 145 ball park.
Another way to get some intuition is to think about the typical range IQs for various professions. As you see below, even for professions with the most intelligent people are still typically well below 145.
1$\begingroup$ I wish mods could upvote an answer multiple times ;-) +1 $\endgroup$– AliceD ♦Jun 9, 2017 at 21:05
$\begingroup$ oof, social scientists will not be pleased with this graph. $\endgroup$ Jul 25, 2020 at 14:36
Consider, a normal IQ score falls between the range 85-115 which is approximately 70% of the population (and only 15% of people have an IQ of 115 or above), while an extended average IQ range tends to encompass those between 80-119 which is "x"% of the population. In order to qualify for the International High IQ Society, one must have an IQ of 125 or above, while entry into Mensa (a High IQ organization that represents the upper 2% of the population) requires an IQ of 2 standard deviations above average (or 130 and above). For the lower end of the bell curve, this will be explored later on in the post (as well as a more proper breakdown of the rest of the distribution).
Now, what do these numbers mean? That is, in principle, what can one do with a 100 IQ? It turns out, many studies have been done linking average IQ scores to completion of College Majors, SAT scores, and GRE (set aside the problematic elements for a moment, of which we can explore later). As for College Majors, studies have revealed a strong correlation for between those who go far into/complete specific college majors and IQ. The breakdown is as follows:
Top End of Spectrum
-Physics & Astronomy (133)
-Mathematical Sciences (130)
-Materials Engineering (129)
-Chemical Engineering (128)
-Other Engineering (128)
-Mechanical Engineering (126)
Bottom End of Spectrum
-Home Economics (106)
-Student Counseling (105)
-Early Childhood (104)
-Social Work (103)
In order to attend College and be successful, it was found that an IQ of 110-115 is standardly required. Now, if a person with a 110-115 IQ attempted to be a Physics & Astronomy major, it has been found that they would quickly run into trouble and likely have to drop out (or fail out) early on. However, they would be successful at other college majors, some of which were listed previously. Then, an individual with a 100 base IQ has been shown to not (currently) be able to attend college successfully.
To put this in practical terms, lets take the example of those with an IQ 2 standard deviations from the norm in the adult population (2% of the population), or Physics & Astronomy combined with Mathematical Sciences Majors (closely followed by Philosophy and certain Engineering Majors, but we will limit our discussion to those past the threshold). This indicates that if we took a random sampling of 100 adults, approximately 2 would have a mind currently capable of the "brain power" necessary to do Complex Analysis or Statistical Mechanics (which is in-line with Senior level Physics or Math major cognitive abilities). As for what a 110 IQ would look like in practical terms, such a person would (currently) struggle tremendously to get a Political Science degree if they were able to attain it at all (IQ 120), while they would be able to get a degree in Business (114), Education (110), ect. See list here for more details: https://thetab.com/us/2017/04/10...
Now, IQ links to Standardized Tests such as the SAT and GRE are quite interesting as well--let us proceed with investigating the case of SAT scores. We will use the 1600 score standard (Note: a link to conversions between 2400 to 1600 score standards will be provided under Sources if one were curious). Consider, a score of 925 on the SAT (is claimed) to translate to a base 100 IQ. Here is an outline mapping out key points on the Bell Curve:
IQ, SAT, Meaning
- 55, 400, Trainable Moderate Mental Retardation
- 66, 525, Mild Mental Retardation
- 75, 630, Borderline Mental Retardation
- 87, 775, Dull
- 100, 935, Average
- 113, 1100, Bright
- 120, 1200, Very Bright
- 130, 1310, Extremely Bright
- 141, 1445, Briliant
- 151, 1575, Very Brilliant
For convenience, a few figures converted to the 2400 point scale (conversion chart here- https://blog.prepscholar.com/new... ):
- 75, 820
- 87, 1020
- 100, 1260
- 113, 1510
- 120, 1670
- 130, 1840
- 141, 2070
- 151, 2340
[Note: There are various IQ scales, some reach to numbers higher well higher to this, this is a Standard Scales, others could be used with similar (though varying in extent) results]
Follow this link to find an IQ Reference Table which outlines IQ ranges and typical corresponding abilities: https://www.easycalculation.com/...
Below is a transcription of the outline (IQ range, Category, Typical Ability):
Profound Mental Retardation
Limited or no ability to communicate, eat, bath, dress and toilet.
Severe Mental Retardation
Limited ability to communicate, eat, bath, dress and toilet. No academic skills.
Moderate Mental Retardation
Some independent self-help skills and very basic academic skills.
Mild Mental Retardation
Usually able to dress/bath independently and can do simple jobs. Elementary school academics.
May live independently with difficulties. Can perform simple and repetitive jobs.
Can complete vocational education and live independently.
Can complete high school graduation and college with difficulty.
Typical level of college graduates.
Typical level of persons with doctoral degrees.
Capable of understanding highly, complex academic material.
intellectual ability and capable of looking beyond known facts.
Extraordinary talent like Albert Einstein
3$\begingroup$ Thanks, and welcome to psych.SE. We do prefer peer-reviewed sources over blogs and such with unknown affiliations. Also, since IQ tests are validated by (calibrated to) academic success, it's no surprise that they correlate well with it, so I am not sure if this really answers the OP's question. $\endgroup$– Arnon Weinberg ♦Feb 25, 2018 at 4:53
2$\begingroup$ As @AaronWeinberg suggests, peer-reviewed sources are preferred over blogs. Can you at least edit your post and change the 6 links for more suitable sources? $\endgroup$ Feb 25, 2018 at 11:33
4$\begingroup$ I understand the preference for peer-reviewed sources, though I would point out the member above my post used one of the exact same sites/sources as I and received praise rather than criticism (which is not peer-reviewed). $\endgroup$ Feb 25, 2018 at 21:31