Alfred Binet, 1857-1911

It's a matter of everyday experience that some people are more intelligent  than others. But what is "intelligence"? And how do we measure it?     In 1905, a French psychologist by the name of Alfred Binet, working with a physician-associate, Theodore Simon, developed the Binet Simon Test designed to measure the intelligence of retarded children, based upon their observations that. (1) Just as children grow taller as they grow older, they grow more mentally capable as they grow older; and (2)  Some children can perform at age and equivalent-grade levels above their chronological ages, while other children perform at age and equivalent-grade levels below their chronological ages. For example, a few 6-year-olds could perform as well on the Binet Simon mental tests as the average 8-year-old, while a few 6-year-olds could only perform as well as the average 4-year-old.

What Is "IQ"?
    It was also observed that the gaps between children's mental ages and their chronological ages widened as the children got older. The 6-year-old with the mental age of 8 had a mental age of 12 by the time he was 9 and a mental age of 16 by the time he was12. Similarly, the 6-year-old with a mental age of 4 had a mental age of 6 when he was 9 and a mental age of 8 when he was 12. In 1912, the German psychologist, William Stern, noticed that even though the gap between mental age and chronological age widens as a child matures, the ratio of mental age to chronological age remains constant (and, as we will see, remains essentially constant throughout life). This constant ratio of mental age divided by chronological age was given the name "Intelligence Quotient". Actually, the intelligence quotient is defined as 100 times the Mental Age (MA) divided by the Chronological Age (CA).

IQ = 100 MA/CA.

In other words, IQ is a ratio.

How IQ Is Distributed in the General Population
    A plot of the frequencies of occurrence of various IQ's in the general population form a bell-shaped  curve (Figure 1, below). As the curve in Figure 1 suggests, most people have IQ's that are fairly close to the average IQ of 100.
    As Figure 1 shows, about 68% of all IQ's lie within 15 IQ points on either side of the average IQ of 100. This means that 32% of the public have IQ's outside the range 85 to 115. About 16%, or about 1 in 6, possess IQ's above 115, and about 16%, or about one in six have IQ's below 85.
    The distribution curve for intelligence is a bell-shaped curve but it is not a Gaussian distribution.
    The lower half of the IQ curve doesn't closely fit any distribution known to me. Presumably, this is because natural genetic endowments are are mixed with special conditions such as Down's Syndrome and phenylketonuria, and with environmental insults, so that the influences shaping the lower half of the curve are more complex than those influencing the upper half of the IQ distribution.
    For the upper half of the curve, the natural logarithms (ln) of the ratios of mental ages to chronological ages form a Gaussian distribution.  Close to the average IQ of 100, the differences are minor between the IQ bell-shaped curve and the (Gaussian) bell curve for the natural logarithms of IQs, but they become quite substantial on the wings of this curves. For example, the predicted frequency of occurrence for someone with an IQ at or equal to 200 is about 1 in 78,000,000,000. The observed frequency of occurrence is about 1 in 500,000, or about 39,000 times greater than a Gaussian distribution would predict.

One Standard Deviation Above the Average  (IQ = 116)
    Approximately 84% of the public has an IQ of 115 or below. Only 16% of the population, or about 1 in every 6 has an IQ of 116 or above.
Two Standard Deviations Above the Average  (IQ = 135)
    Approximately 98% of the public has an IQ of 134 or below. Only 2% of the population, or about 1 in every 50 (the entry level for Mensa), has an IQ of 135 or above.
Three Standard Deviations Above the Average  (IQ = 157)
    Approximately 99.87% of the public, has an IQ of 156 or below.  Only about 0.13%  or about 1 in 750,  own IQ's at, or above 157. (There would be about 360,000 such individuals in the United States, or about 400,000 in the United States and Canada.)
Four Standard Deviations Above the Average  (IQ = 182)
    Approximately 99.997% of our population has an IQ of 181 or below. Only 0.003% or about 1 in 30,000 possesses an IQ of 182 or above. (There would be about 9,000 such individuals in the United States, or about 10,000 in the United States and Canada.)
Five Standard Deviations Above the Average  (IQ = 212)
    Approximately 99.9997% of our population has an IQ of 211 or below. Only 0.0000287% or about 1 in 3,500,000 can boast an IQ of 212 or above. (There would be about 77 such individuals in the United States, or about 15 in the United States and Canada.)
Six Standard Deviations Above the Average  (IQ = 246)
    Approximately 99.99999990% of the world's population lies below an IQ of 246. Only about 1 in 1,000,000,000 , or about six people on Earth can claim an IQ this high. (We might expect to find 1 such person in Europe, North America, and Australia, New Zealand, and South Africa, with the rest residing in the rest of the world.)

    The above numbers must be taken with a pinch of salt. For example,

• The Jewish have higher IQ's (especially verbally) than most other ethnic groups. 
• The Japanese are rumored to have IQ's that are higher than those found in the West. 
• Orientals in general are alleged to score exceptionally well on non-verbal tests. (And of course, it's harder to compare verbal capacities across different cultures.) 
• In one comparison of average IQ's among European nations, Belgium scored at the top.  
• The Flynn Effect is raising new questions regarding IQ's. For example, because of the Flynn Effect, the IQ of someone at the 200 level would seemingly drop to, perhaps, 167 over a period of 50 years when compared with young adults with a 200 IQ. (This would be in addition to any age-related cognitive declines.)

    Consequently, until these loose threads can be better sorted out, the above numbers, while they are approximately correct, are subject to refinement.

    The smartest person in the U. S. and Canada would be expected to have an IQ of about 238. Keith Raniere is said to have scored 242 on a childhood IQ test (private communication). Marilyn vos Savant established a Guinness Book of World Records record of 228 (a category which has since been retired). 

Mental Age for Adults
    At the end of adolescence, mental age, like height, stops increasing rapidly. Until 1960, it was customary to use 16 as the divisor for mental age among adults. Actually, certain mental functions increase slowly and slightly after the age of 16, peaking in the 20's, with others remaining stable or even rising slightly up to the age of 60 or so. With some individuals, vocabulary may increase over time.

The Practical Significance of IQ
    The average IQ of the population as a whole is, by definition, 100. IQs range from 0 to above 200, and among children, to above 250. However, about 50% of the population have IQs between 89 and 111, and about 80% of the population have IQs ranging between 80 and 120, with 10% lying below 80, and 10% falling above 120.
    For IQs below 120, IQ is the best predictor of socioeconomic status of any psychometric measurement. In more complex jobs, IQ is better than even education or experience at predicting job performance. In her article "The General Intelligence Factor", Scientific American Presents "Exploring Intelligence", pg. 24, 1999, Linda Gottfredson states,
    "Adults in the bottom 5% of the IQ distribution (below 75) are very difficult to train and are not competitive for any occupation on the basis of ability. Serious problems in training low-IQ military recruits during World War II led Congress to ban enlistment from the lowest 10% (below 80) of the population, and no civilian occupation in modern economies routinely recruits its workers from that below-80 range. Current military enlistment standards exclude any individual whose IQ is below about 85."
    "Persons of average IQ (between 90 and 100) are not competitive for most professional and executive-level work but are easily trained for the bulk of jobs in the American economy. By contrast, individuals in the top 5 percent of the adult population can essentially train themselves, and few occupations are beyond their reach mentally."
    "People with IQs between 75 and 90 are 88 times more likely to drop out of high school, seven times more likely to be jailed, and five times more likely as adults to live in poverty than people with IQs between 110 and 125. The 75-to-90 IQ woman is eight times more likely to become a chronic welfare recipient, and four times as likely to bear an illegitimate child than the 110-to-125-IQ woman."

    In his book, "Straight Talk About Mental Tests", The Free Press, A Division of the Macmillan Publishing Co., Inc., New York, 1981, pg. 12, Dr. Arthur Jensen cites the following four IQ thresholds:
(1) An IQ of 50 or below. This is the threshold below which most adults cannot cope outside of an institution. They can typically be taught to read at a 3rd or 4th grade level. However, they cannot normally function in the customary classroom setting, and they require special training programs.
(2) An IQ between 50 and 75. At this level of intelligence, they generally cannot complete elementary school. Most adults will need smarter help in coping with the world.
(3) An IQ between 75 and 105. Children in this IQ range are not generally able to complete a college prep course in high school.
(4) An IQ between 105 and 115. May graduate from college but generally, not with grades that would qualify them for graduate school.
(5) An IQ above 115. No restrictions.
    For IQs in these ranges, the influence of IQ upon socioeconomic status is dramatic. 31% of those with IQs below 75 were on welfare, compared with 8% of those in the 90 to 110 IQ interval, and 0% in those with IQs above 125. 55% of mothers with IQs below 75 went on welfare after the birth of the first child, compared with 12% of those with IQs between 90 and 110, and 1% of those with IQs above 125. Income is highly dependent upon IQ up to an IQ-level of about 125.

Table 1 - Practical Significance of IQ

IQ Range	Frequency	Cumulative Frequency	Typical Educability	Employment Options
Below 30	>1%	>1% below 30	Illiterate	Unemployable. Institutionalized.
30 to 49	>1%?	>1% below 50	1st-Grade to 3rd-Grade	Simple, non-critical household chores.
50 to 59	~1%?	1.5% below 60	3rd-Grade to 6th-grade	Very simple tasks, close supervision.
60 to 73	3.5%?	5% below 74	6th-Grade to 8th-Grade	"Slow, simple, supervised."
74 to 88	20%	25% below 89	8th-Grade to 12th-Grade	Assembler, food service, nurse's aide
89 to 100	25%	50% below 100	8th-Grade to 1-2 years of College.	Clerk, teller, Walmart
100 to 111	25%	50% above 100	12th-Grade to College Degree	Police officer, machinist, sales
112 to 120	15%	25% above 111	College to Master's Level	Manager, teacher, accountant
121 to 125	5%	10% above 120	College to Non-Technical Ph. D.'s.	Manager, professor, accountant
126 to 131	3%	5% above 125	Any Ph. D. at 3rd-Tier Schools	Attorney, editor, executive.
132 to 137	1%	2% above 132	No limitations.	Eminent professor, editor
138 to 150	0.9%	1% above 137	No limitations.	Leading math, physics professor
151 to 160	0.09%	1 in 1,100 above 150	No limitations	Lincoln*, Copernicus*, Jefferson*
160 to 176	0.009%	1 in 11,000 above 160	No limitations	Descartes*, Einstein*, Spinoza*
177 to 200	0.0009%	1 in 1,000,000 above 176	No limitations	Shakespeare*, Goethe*, Newton*

* - Note that these men are assigned different IQs depending upon who is estimating their IQs.Einstein was exceptionally strong in math and logic, and relatively weak verbally. (These IQ's are based upon a standard deviation of 16.) Also, these estimated IQs would be subject to the Flynn Effect. 

Wandering Down to Walmart
    To gain a clearer perspective regarding what this means in terms of our daily contacts with people, let's take a trip down to a local Walmart. Let's suppose we're visiting the only Walmart in a small, rural town, so that neighborhood inhomogeneities don't affect the cohort of shoppers we'll find at the store. That way, we'll be seeing a nearly random cross-section of the public on our trip.
    OK. Here we are at Walmart. I can already see quite a few people out here in the parking lot.
    Let's suppose that we're going to see 100 other customers while we're here shopping (with, perhaps,  about 60 to 70 cars in the parking lot), and then consider their breakdown by IQ. On the basis of the law of averages, we'd expect to see one person here with an IQ below 64. There'd be someone else with an IQ between 64 and 68. There should be 3 more with IQs between 69 and 75. In other words, if this is a random crowd, 1 out of 20 people we're going to meet will have IQs below 75, and will be retarded. Keep your eyes peeled. See if you can spot 'em. About 1 out of 10 people we'll walk past here at Walmart has an IQ below 80, or about 10 of the 100 people who cross our paths here in the store. Hey, look! Does she look kind of sagaciously-challenged to you? One out of 5, or 20 of the 100 people we're seeing have IQs below 87, with about 1 in 10 in the 80 to 87 IQ range. Half the crowd, or 50 out of the 100, has below-average intelligence. And of course, the other half has above-average intelligence. Twenty of them (1 out of 5) have IQs above 113. Ten of them, or 1 in 10, have IQs above 120. Five of them have IQs above 125, and have the potential to become university professors with Ph. D's. Two of them have IQs of 132 or above, and are potential members of Mensa. One of them has an IQ above 136.
    Did you spot them? I saw one or two possible candidates, but I suppose we'd better not walk up and say,
"Pardon me, ma'am. You look mentally challenged. Are you?"
    She might hit us with her purse.
    If we spent time at a large urban mall, we might rub elbows with 1,000 shoppers. In an average, unenriched setting, where we saw 1,000 other shoppers at Christmas-time, IQs might typically be expected to range between 50 and 150. In a blue-stocking suburb like Norcross, Georgia, or Corte Madera, California, we might expect to find one or more folk with IQs above 150, and perhaps, an individual or two with an IQ above 160. This is a huge range of IQs.
    I think that the range of intellects that we walk past in the world is awesome. The span between top and bottom among 100 people chosen at random would be about 75 points of IQ. And we've been walking past them every day.
    Until I wrote this up this afternoon, I had never stopped to think just what intellectual diversity awaits us at our local shopping centers. Half the people we meet in cars on the road have below-average intelligence, and 1 in 20 must be seriously retarded, with a mental age of 12 or below. It's a tribute to every driver that we do so well on the road.

High-IQ Societies
    One High-IQ organization that has no entrance requirements is the Vitruvian Society.
    Individuals with IQs of 132 or above may join Mensa upon presentation of qualifying test results. Individuals with IQs of 137+ are eligible to join organizations such as TOPS (Top One Percent Society) and Intertel. An IQ of 141 and above will admit them to Colloquy. Those with IQs of 150+ qualify for membership in the Triple-Nine Society, the SesquIQ, the IQuadrivium Society and the One-in-a-Thousand (OATH) Society, those with IQs of 164 or above are potential candidates for the Prometheus Society and the Ultranet, and those rare specimens with IQs above 176 are welcomed into the Mega and Pi Societies.  There is even a Giga Society for the handful of people in the world (six) who qualify at the one-in-a-billion level. Needless to say, at the one-in-a-million level, the membership roster is somewhat exiguous. 
    Some of these organizations are also open to subscribers. Subscribers are not allowed to vote, but they may participate in the fascinating dialogues that take place within these societies.

Deviations from a Bell-Curve
    IQs near the center of the range, between about 75 and 125 are well-represented by a bell curve like the one shown below. However, IQs below about 75 don't fit a bell curve well at all. The reason is that there are some individuals who suffer brain damage and who increase the pool of the seriously retarded. Similarly, it was discovered in 1921, when 250,000 California schoolchildren were screened with IQ tests to determine whether they should be included in the Terman Study of gifted children, that there are a lot more very high IQ score than would be predicted by the bell-curve. For example, the Terman Study found 77 children with IQs of 170 or above, where they would only have expected to find 1 or 2. They found 26 children with IQs of 180, where theory would have predicted only one child with an IQ above 180 in 3,000,000 children. They found one child with an IQ of 201, where the bell-curve predicts only one such child out of every 5,000,000,000 children. Part of this is thought to be a result of uneven rates of mental growth. Some children experience temporary spurts of mental growth that are later offset by temporary slackening of mental development--like children that physically-mature relatively early. Part of it is also a function of the fact that, if there are 4 or 5 children with IQs in the mid-190's (because of "growth spurts"), one of them may have an especially good day and score 5 or 6 points higher than he would normally score, while another of them on that same day might score 5 or 6 points lower than she would usually score. The one that scores higher is the one that catches our attention.

Deviation IQs
    Because of these effects, beginning around 1960, psychometrists defined adult scores in terms of percentiles, and then translated those percentiles into the IQ scores that the bell-curve predicts. These percentile-derived scores are called "deviation IQs", and the older (mental age)/(chronological age) IQs are called "ratio IQs". (For a more-complete description of deviation IQs versus ratio IQs, click here.This had the effect of reducing IQ scores, since ratio IQs tend to run quite a bit higher at the higher levels than do deviation IQs. (The highest probably deviation IQ is about 200, since a deviation IQ of 200 would be expected, as mentioned above, to occur only once in every 5,000,000,000 people--the approximate current population of the earth.) The scale shown below the plot presents one approach--(a log-normal conversion)--to estimating the ratio IQs that correspond to given deviation IQs.

The figure below shows the upper half of the "bell-curve" distribution (Gaussian normal distribution) of human intelligence. As the plot shows, 50% of the population has below-average intelligence. As the bell-curve below indicates, 1 person in 10 has an IQ of 120 or above, 1 in 20 boasts an IQ of 126 or above, 1 in 50 is Mensa level, with an IQ of 132 or above, 1 in 100 possesses an IQ of 137 or above, 1 in 1,100 is characterized by an IQ of 150 or above, 1 in 11,000 sports an IQ of 160 or above, 1 in 1,000,000 owns an IQ of 176 or above, and so forth.
 

How Is IQ Measured?
    There are a number of IQ tests available. Some IQ tests are untimed, individually administered tests such as the Stanford-Binet and the Wechsler tests. (The five Wechsler Performance subtests are timed.) Other tests are timed, proctored group tests, such as the Raven Progressive Matrices, the California Test of Mental Maturity (CTMM) and the Cattell Culture-Fair Test, which are easier to administer but are narrower in scope. (Included in this group would be the Scholastic Aptitude Test, the Graduate Record Exam, the Miller Analogies.) Still a third class of test is the power test, such as the Mega Test, the Titan Test, and the Test for Genius. These are unproctored, open-book tests in which the test-taker lays protracted siege to difficult problems that emulate the kinds of problems encountered in actual research. These tests are not universally recognized as true IQ tests because it is felt that they are susceptible to cheating. and that their scores depend upon collatoral factors such as persistance and library skills as well as sheer intelligence.
    IQ tests have been under attack since their inception. It is, perhaps, counter-intuitive and unpopular that a test requiring an hour or two can establish the upper bounds of one's intellect for a lifetime. However, although they're not infallible they do a remarkably good job of generating a score that will remain more or less constant throughout life.

Can Intelligence Be Measured With a Single Number?
    Yes and no. One of the most serious criticisms of using a single number to assess intelligence is that people may be stronger in certain areas such as verbal skills, logical aptitude or spatial visualization than in others. Drs. Richard Feynmann and Albert Einstein would be examples of geniuses who were extremely strong mathematically while being relatively weak verbally. More  commonly, though, purely intellectual abilities tend to be uniformly high or uniformly low in a given individual, leading to the concept of an underlying "g" or "general intelligence" that powers all the specialized intellectual aptitudes. Still, this doesn't happen with everyone, and the exceptions, like Richard Feynmann and Albert Einstein, are very important. Tests like the Wechsler Adult Intelligence Scale (WAIS) consist of a number of subtests that are scored separately and can measure the profile for an individual. (Dr. Howard Gardner has defined seven types of intelligence, while Dr. Robert Sternberg has identified three.)
    It's also easier to make an IQ score that's lower than your true IQ than it is to make a score that's higher. Taking a test on a bad day, or spending too much time on a few difficult items could artificially lower one's score. The best results are obtained when more than one test is administered.

What Does Adult IQ Mean?
    Generally, one's mental age stops rising rapidly when one reaches the latter teens--e. g., 16. Consequently, on some IQ tests, "16" was taken as the chronological-age divisor in an IQ calculation for adults. The Wechsler Adult Intelligence Scale is calibrated for all ages up to 70, with chronological-age divisors appropriate to every age 70 or below.
    The average IQ is, by definition, 100. To get an idea what this means, someone with an IQ of 80 or below is considered to be marginally able to cope with the adult world. People with IQ's of 80 or below typically work as unskilled laborers such as lawn maintenance and trash pickup. They generally need help from friends or family to manage life's complications. About 10% of the population has an IQ of 80 or below.
    People with IQ's of 80-90 are a little on the slow side but may be found in fast-food restaurants, day-care centers, etc. They may also be found in unskilled jobs. About 16% of the population has IQ's in this range.
    People with IQ's of 90-110 generally occupy semi-skilled positions, including typists, receptionists, assembly line workers, and checkout clerks. They are able to keep up with the world, and comprise about 46% of the public.
    People with IQ's in the 110 to 120 range fill the skilled trades and include some tool and die makers, teachers, and Ph. D.'s among their ranks. They also make up 16% of the population.
    People with IQ's of 120 and above tend to staff the professions as doctors, dentists, lawyers, teachers, and college professors. They fall in the upper 10% of the population.
    Note that there are lots of exceptions...  many, many people working in jobs for which they are overqualified. For example, there are waiters and waitresses who are working their way through college. One member of the Mega Society is employed as an alarm technician.

    The average IQ of all college professors is 130, which lies within the upper 3% of the general public.