|A portion of the modern IQ scale (2017), originally developed in 1916 by Lewis Terman, showing IQs ranging from 26 to 160.|
In fiction, a few examples are, at the low end, the character Forest Gump, who, as a child with IQ of 75, was below the 80 or above level for normal students, and thereby was mandated by the stated to be put into the special education class. At the high end is the character Eddie Morra (played by Bradley Cooper) of the 2011 film Limitless, claims an “four digit IQ” or IQ:1,000+
The modern IQ scale was conceived between 1916 and 1926 by Stanford psychologists Lewis Terman and Catherine Cox who set the scale, as shown adjacent, approximately:  A more recent distinction, as added above, is the standard IQ cutoff for a child to get into a gifted program is 130. 
The world’s first intelligence measuring device was the Binet-Simon intelligence scale published in 1905 by French abnormal child development psychologists Alfred Binet and Theodore Simon, originally designed to test for “inferior states of intelligence”, so to diagnose and thus facilitate the education of the subnormals, categorized as either: idiot (lowest state), imbecile (intermediate low state), and moron (state nearest normality). 
In 1912, William Stern, a German psychologist, added to Binet's work by inventing the concept of "mental quotient", defined as the ratio of the age the test was designed for divided by the age of the person who takes the test. Thus, for instance, if a eight-year-old took a test designed for a ten-year-old, and passed, the child's MQ would be 1.25 or ten divided by eight.
In 1916, Lewis Terman, a professor at Stanford University, modified Stern's formula by multiplying it by 100, creating a new formula, 100(MQ) that he called an "intelligence quotient" thus setting the person's intelligence at a value of 100, values below being indicative of reduced average intelligence, values above being indicative of above average intelligence. Terman, however, failed to speculate as to what formulaic values above 140 would mean except that it would be the genius range.
In the 1920s, Terman assigned his new graduate student Catherine Cox the job of assigning IQ values to the world's greatest geniuses, so to affix the top of his IQ scale to recognizable points or intellects. Cox published her results in her 1925 PhD dissertation "On the Early Mental Development of a Group of Eminent Men" and the following year, the now-famous 1926 book Early Mental Traits of 300 Geniuses, which presented an in depth formulaic IQ ranking of the top 300 geniuses who were at adult age between the years 1450 and 1850, setting the ceiling genius IQ value of 210 to German polymath Johann Goethe.
|French psychologist Alfred Binet (1857-1911): in 1899 was appointed to the Commission for the Retarded, a repercussion of a new French law that mandated school for children ages six to fourteen, whose aim was to develop a test to differentiate between normal and abnormal children, so to be able assign each to different classrooms. ||French psychologist Theodore Simon (1872-1961): was an intern at the asylum in Perray-Vaucluse, studying abnormal children, during which time he began to work with Binet to develop a test that could measure intellectual development of children ages 3-12.||German psychologist William Stern (1871-1938): reviewed the work of Binet (and others), and developed the idea of expressing intelligence in the form of a single number, the "mental quotient" (1912) as one’s mental age divided by one’s chronological age:  ||American psychologist |
Lewis Terman (1877-1956): refined the Binet-Simon scale (1916) to focus on testing the ‘average’ student and used Stern's proposal that an individual's intelligence level be measured as an IQ: idiot (below 20), imbecile (20-49), moron (50-69), deficient (70-80), dull (80-90), normal (90-110), smart (110-120), superior (120-140), genius (140 and over). 
|American psychologist Catherine Cox (1890-1984): completed her PhD with a dissertation “On the Early Mental Development of a Group of Eminent Men” (1925) under Terman and expanded this into the 1926 book Early Mental Traits of 300 Geniuses, in which she assigned IQ values to the top 300 geniuses who lived between 1450 and 1850, setting the ceiling genius IQ of 210 to Goethe. .|
In sum, the modern intelligence test was developed by Stanford psychologist Lewis Terman, beginning in 1911 and first published in 1916, called the Stanford-Binet scale, a modification of the Binet-Simon scale, albeit focused on testing the 'average' person. The original Stanford-Binet (score range: 0-168) was designed so that the average person would score 100, with two-thirds scoring between 85 and 115.  Scores from the Stanford-Binet were then multiplied by German psychologist William Stern's "mental quotient" (age the test was designed for divided by actual age) to give an IQ, according to the following formula (shown below with a score of 100): 
In short, the age of designed test (e.g. a Stanford-Binet test designed for 12-year-olds) would be divided by actual age (e.g. age 8) of the tester multiplied by 100 (or possibly the score received) then . This original IQ formula is said to work fairly well for children but not for adults. An 8-year-old who scores a 100 on a Stanford-Binet (designed for 10-year-olds) would thus be said to have an IQ of 125 = (10/8)*100. Yet a 40-year-old who scores 100 on the same test would yield a nonsense value of IQ of 25 = (10/40)*100.
|Sample Binet-Simon question for five-year-olds called “copying the square”, where the tester draws a square, 3 or 4 cm on each side, and asks the child to copy it using a pen. Versions 1-3 would be considered satisfactory, whereas versions 4-6 would constitute failures.|
In other cases, specifically, those who score answer all the questions correctly, at a young age, the resultant value is far skewed. The over-estimated IQ of 325 for Michael Kearney, for example, was derived from a score of 168 on a Stanford-Binet test designed for children aged 6 or above. Taken literally, this would correlate to an IQ of 252 = (6/4)*168. Kearney's parents, however, claim they calculated an IQ of 325 using instructions on how to do the age ratio at their local library. The only way to arrive at a value such as this would be to assume a 'mental age' of 7.74-years, which would give an IQ of 325 = (7.74/4.0)*168, assuming he was exactly four-years old at the time of the test. This nonsensical IQ value of 325 (115 points higher than the Cox ceiling genius IQ of 210), however, does not corroborate with Kearney receiving a 3.6 GPA in a relatively easy subject of anthropology at a average-ranked college (University of South Alabama) six years later.
An example question to test for supposed ‘normalcy’ of four-year-olds is the question: “are you a little boy or a little girl?” When asking four-year-olds this, not all will answer correctly; sometimes the child will simply say ‘yes’ or ‘no’. A normal four-year-old, according to Binet and Simon, however, will always answer correctly when asked its sex. An example five-year old test is called copying the square, where the child is instructed to reproduce a drawn square, as depicted adjacent. The following example questions (1911 version) were added by Terman to Binet’s original IQ test to create the "Stanford-Binet test":
Question #1: An Indian who had come to town for the first time in his life saw a white man riding across the street. As the white man rode by, the Indian said - “The white man is lazy; he walks sitting down.” What was the white man riding on that caused the Indian to say, “He walks sitting down.”
Terman explained that the correct response is: “bicycle.”; whereas incorrect responses include: tricycle, unicycle, horse, wheelchair, rickshaw, automobile, or motorcycle.
Question #2: My neighbor has been having queer visitors. First a doctor came into the house, then a lawyer, then a minister. What do you think happened there?
In this case, Terman explained that a satisfactory answer must normally involve a death: “The doctor came to attend a sick person, the lawyer to make a will, and the minister to preach the funeral.” The following answer was failed by Terman: “Someone was sick; the lawyer wanted his money, and the minister came to see how he was.”
Guinness book IQ
To give an example of how answering these questions can yield an IQ score, to create the infamous "230" IQ score boasted by Marylin vos Savant, as published in the 1986 Guinness Book of World Records, in 1956, at age 10, she correctly answered all of the questions, such as those above, on the Stanford-Binet, which is designed for people up to age 23 or specifically 22-years 10-months (22.83 years), thus her ratio IQ (see below) at age 10 was determined as: IQ = (22.83/10)*100 = 228.3. Here we see a nonsensical calculation. According to Cox, an IQ of 190 is a genius intelligence on par with Newton. Yet vos Savant, who according to the Terman IQ formula has a 228 IQ, became pregnant at 16, later a college dropout, and careered as a news paper columnist, and thus may be a smart person, but certainly no Newton. To illustrate further issues with the Terman IQ formula, if Savant retook the Stanford-Binet test at age 40, scoring a perfect score again, it would tell us she has an IQ of 57 = (22.83/40)*100 used the same formula at age. In this context we see the issue with ratio determined IQs, in that answering a collection of trivial Stanford-Binet type questions does not make a 10-year old the world's smartest person.
Buzan IQs are those determined by English accelerated-learning expert Tony Buzan and English chess grandmaster Raymond Keene in 1994, using a method independent to that of Cox, in which they scored the top 100 leading minds on an 835-point scale (GS=Genius Score): dominance in the field (100), active longevity (100), polymath (100), versatility (100), strength and energy (100), IQ (100), ongoing influence (100), prolificness and achievement of prime goal (100), universality of vision (15), outstanding originality (10), deliberate desire to create teaching avenues or academies to further the genius’ ideas (10). 
(a) IQs shown in Italics in the above table were determined via the less-accurate estimated Stanford-Binet ratioed IQ formula method, discussed above. This formula can then further vary according to both the score of the test used and the test given, which combined can give various ratio IQ scales. Using this scaling, if a young child gets a perfect score on, for example, the Stanford-Binet (168), extropolative ratio IQs can be determined well above 200 and near to 300 if child in in the low to mid single digits in age.
(b) Ratio IQs, to note, can be very inaccurate, may vary depending on reference, and calculations of which can give quite skewed IQ approximations.
(c) Michael Kearney (as discussed above), to cite an example, had his IQ, at age four, age-ratio scored at 325, based on a 168 test score (maximum possible), according age-ratio calculations done by his parents in their local library. The Stanford-Binet L-M version measures a mental age that can then be adjusted for a child's chronological age to obtain a true IQ. Using the above formula, a 325 ratio-score would correspond to a mental age of 13-years. If the ratioed IQ were correct, Kearney should be smarter than anyone alive. Yet, six years later, he obtained a 3.6 GPA in a relatively simple subject (anthropology), at an average ranked school (University of South Alabama); thus putting him in the slightly above average college graduate IQ range (110-115).
● IQ scale
1. Note: This page lists the references to the IQ: 200+ (and IQ: 225+) page. These were put on a separate page owing to the fact that the EasyEdit tool bar, to this wiki, stops working when a wiki page gets past the circa 26-30 page mark.