"Mental Age"

Alfred Binet, 1857-1911

It's a matter of everyday experience that some people are smarter than others. But how do we measure "smartness"?     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.     In 1911, the concept of "mental age" (as distinguished from "chronological age")

was introduced. The 6-year-old who performed as well as the average 8-year-old was assigned a mental age of 8, while the 6-year-old who performed only as well as a 4-year-old was assigned a mental age of 4.

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.

Mental Age for Adults
    At approximately. the age of 16, mental age, like height, stops increasing. 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 sttus 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 50	>1%?	>1% below 50	1st-Grade to 3rd-Grade	Simple, non-critical household chores.
50 to 60	~1%?	1.5% below 60	3rd-Grade to 6th-grade	Very simple tasks, close supervision.
60 to 74	3.5%?	5% below 74	6th-Grade to 8th-Grade	"Slow, simple, supervised."
74 to 89	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	50%	1 in 2 above 100	12th-Grade to College Degree	Police officer, machinist, sales
111 to 120	15%	1 in 4 above 111	College to Master's Level	Manager, teacher, accountant
120 to 125	5%	11 in 10above 120	College to Non-Technical Ph. D.'s.	Manager, professor, accountant
125 to 132	3%	1 in 20 above 125	Any Ph. D. at 3rd-Tier Schools	Attorney, editor, executive.
132 to 137	1%	1 in 50 above 132	No limitations.	Eminent professor, editor
137 to 150	0.9%	1 in 100 above 137	No limitations.	Leading math, physics professor
150 to 160	0.1%	1 in 1,100 above 150	No limitations	Lincoln, Copernicus, Jefferson
160 to 174	0.01%	1 in 11,000 above 160	No limitations	Descartes, Einstein, Spinoza
174 to 200	0.0099%	1 in 1,000,000 above 174	No limitations	Shakespeare, Goethe, Newton

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, 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 seriously retarded! (I guess we're lucky the world works as well as it does.) 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 or Corte Madera, 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 deviation IQ, or more than 80 points of ratio IQ. And we've been walking past them every day.
    This isn't the whole story. It's mentioned below that even on culture-fair tests, the average IQ of our African-American population falls about one standard deviation below those of the other components of our population. This means that 1 out of 10 African-Americans has an IQ below 59, and only about 2 Africans in 1,000 can qualify for Mensa. So most probably, on our trip to Walmart, we're going see an African-American with an IQ of 60 or below (mental age of 10).
    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. Ouch! I think I'll ride my bike on back streets to the store.

Race, Ethnicity, and Gender
    There are significant variations in the distributions of IQ as we switch among races, ethnic groups, and gender. In discussing this area, I'm presently skating on thin ice because I'm relying on recalled information. I'll try to pin this down within the next few weeks, so if you would, please regard what I'm about to say as an unconfirmed "placeholder" for what I hope will be more-reliable information a week or two from now.
    Fifty years ago, it was thought that American Indians had an average IQ of about 69, but I have the impression that this is now considered to be a vile canard. American Indians appear to have an average-IQ equal to approximately 100. Sinic people reared in the United States have an average IQ if about 103(?), with an average IQ of the order of 106 when reared in Japan. They consistently show relatively higher mathematical and spatial-visualization scores and relatively lower verbal scores than their Caucasian counterparts. African-Americans have a population-average IQ that has remained consistently about one standard deviation or 16 points below the U. S. Caucasian mean of 100 (for an average IQ of 84).
    Having condemned African-Americans to this racially inferior estate, let me bring up the good news.
(1) If the Flynn Effect is real, African-Americans in 2000 have IQs as high as Caucasians in 1950, and hey! we didn't consider ourselves to be slow learners. Today's African-Americans have IQs as much as 15 points above the average Caucasian in 1900.
(2) A year ago, a Johns Hopkins spokeswoman, speaking to the parents of profoundly gifted children, told them that, based upon the nootropic ("smart pill") pharmaceuticals that are now entering the FDA pipeline, it should be possible to boost children's IQs by as much as 50 points by 2010. A memory enhancement pill is on its way to market over the next few years which would allow total memorization in long-term memory over a 3-to-4-hour period.
(3) Genetically engineered boosts in intelligence should be technically feasible within the next decade or two.

High-IQ Societies
    As mentioned previously, 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). Those with IQs of 150+ qualify for membership in the Triple-Nine 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--one-in--billion--Society, with two members, plus its founder.) Needless to say, at the one-in-a-million level, the membership roster is somewhat exiguous. 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.

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