# IQ Range

The terms IQ stands for ‘Intelligence Quotient’, and is derived through a series of tests to obtain an estimatolde of an individual’s cognitive ability (or as a rough proxy of an individual’s general intelligence – “G”).The IQ score was historically a quotient (i.e. a fraction) that was obtained by dividing an individual’s Mental Age (MA) by that person’s Chronological Age (CA) and multiplying by 100. The MA was derived from a series of mental tests and tasks. This was the predecessor method to calculating modern IQ test scales.

So for example: If a five year old girl (let’s call her Liz) was able to perform the mental tasks and tests as well as an average seven year old, then her Mental Age (MA) was calculated to be 7. Under the historical method, Liz’s IQ would have been (MA / CA) x 100 = (7 / 5) x 100 = 140. In other words, she would have been considered mentally advanced or “intelligent” for her age.

By the start of World War II, some IQ pioneers replaced the old ‘quotient’ method with Standard Scores, which were statistically much more robust and eliminated several problems under the quotient method. New IQ test scales were born.

As hundreds of thousands of tests had already been administered by this time, it emerged that across a population, IQ scores followed a normal distribution, and thus allowed for the natural upgrade to the use of standard scores. A normal distribution can be described using only two variables: the mean and the standard deviation. For simplicity, the mean was set to 100 (which is consistent with the predecessor idea of people’s MA=CA on average), and the standard deviation will depend on the IQ test administered. Note that some of the most influential IQ tests have a Standard Deviation of 15, 16 or 24, which means that an IQ score alone is meaningless unless accompanied by its standard deviation.

## IQ Score Chart

The observation that IQ followed a normal distribution was revolutionary as it became possible to describe what the population distribution of IQs would looks like with the knowledge of only two variables: Mean (or average) and Standard Deviation (or SD).

IQ scoring charts follow a normal distribution which looks like this:

If the mean and standard deviation of a population are known (e.g. mean is = 100 and SD is = 16), then the following should also hold true:

• 68.3% of all test takers should score within 1 SD of the Mean (i.e. IQ between 84 and 116)
• 95.4% of all test takers should score within 2 SD of the mean (i.e. IQ between 68 and 132)
• 99.7% of all test takers should score between 3 SD of the mean (i.e. IQ between 52 and 148)

## IQ score chart and classifications

As stated in the previous section, most people (about 68%) will score within 1 SD of the mean of 100. As you move away from the mean in either direction, there are fewer and fewer people who achieve very low or high scores.

The following tables shows what proportion of the population is expected to score within a particular IQ range.

IQ range (16 SD) Classification Population distribution
130+ Very Superior 2.6%
120-129 Superior 7.5%
110-119 High Average 16%
90-109 Average 47.2%
80-89 Low Average 16%
70-79 Well below average 7.5%
69 and below Lower Extreme 2.6%

## IQ Score range

People very too often state their IQ score without specifying the standard deviation (SD) of the test they have taken. When standard scores were introduced between the end of WWI and the 1960s in the United States, it had been noted across millions of tests observations that the actual calculated standard deviation of test scores was 16. For this reason, IQ-Brain.com has adopted 16 as the standard deviation for its tests and to calculate IQ levels and charts. Now that you know about standard scores, if the mean (or average) of the test is set to 100, and the SD is 16, and combined with the assumption normality, we know that:

• 68.3% of all test takers should score within 1 SD of the Mean (i.e. IQ between 84 and 116)
• 95.4% of all test takers should score within 2 SD of the mean (i.e. IQ between 68 and 132)
• 99.7% of all test takers should score between 3 SD of the mean (i.e. IQ between 52 and 148)

However, many psychologists who were not so good in math began adopting 15 as the standard deviation because of the simplicity of the number. With mean=100 and SD=15, then it follows that:

• 68.3% of all test takers should score within 1 SD of the Mean (i.e. IQ between 85 and 115)
• 95.4% of all test takers should score within 2 SD of the mean (i.e. IQ between 70 and 130)
• 99.7% of all test takers should score between 3 SD of the mean (i.e. IQ between 55 and 145)

Nice round IQ numbers!

The following table will also illustrate the importance of SD. Mensa accepts a variety of IQ test for admission into their society. Of all the tests that are accepted (many of which have very different standard deviations), the only requirement for membership is that the applicant’s score be in the top 2% of the population (i.e. the 98th percentile).

Suppose that there are three applicants, each with a reported IQ score of 130 but achieved on different IQ tests. The following table shows the corresponding percentile for this score based on the standard deviation of each test.

Applicant Test Type IQ Score SD of test taken 100 – test score percentile Admit to Mensa?
Liz Weschler (WAIS-IV) 130 15 2.28% Yes (by a hair)
Pierre Culture-fair scale 130 16 3.07% No
Chen Cattell IIIb verbal 130 24 10.56% No

I hope the above table shows you what each of these applicants claiming that they have an IQ of 130 is meaningless without also mentioning the standard deviation!

## What is the importance of IQ?

Although IQ is not a perfect measure of intelligence, it represents a good proxy of general intelligence. A higher IQ has been shown to positively correlate with several important, real-life variables including:

• Success in relationships including marriage
• Success is the workplace. IQ testing is often used as a recruitment tool in several countries including China, Spain and France. Several researchers have argued that IQ testing remains a better predictor of success at work than other assessment tools (especially unstructured interviews)
• Wealth and lifetime earnings. For instance, the IQ of self-made millionaires is estimated at around 115, while this increases to 120 for self-made billionaires

Similarly, IQ correlates negatively to the following variables:

• Living in poverty
• Having illegitimate children
• Being incarcerated
• Remaining unemployed for long stretches of time

REMEMBER that correlation does not imply causation but merely represents an association, or how two variables move together.

Importantly, IQ testing does not measure practical intelligence or creativity (Sternberg, 1988), The bottom line is that a high IQ does not guarantee success, but it probably means that such individuals may need to work less hard than people with lower IQ to achieve the same result when intellectual output is required. High IQ individuals should not ‘waste’ this natural ability and should strive to apply it to whatever it is that they seek to do.

Conversely, people with lower IQs are not doomed to failure, but may on average need to work harder to be successful in their intellectual pursuits. It is not to say that having an IQ of 105 (i.e. normal intelligence) would make it impossible to become a professor in Chemistry and to publish in scholarly journals, although on the whole, lower IQ persons will probably face a steeper uphill journey than their higher IQ counterparts striving for the same goal.

## What is a high IQ Society

A high IQ society is a private association of individuals who are joined in a society by way of having achieved a certain pre-determined IQ score on a recognized IQ test. There are several famous high IQ societies, and a multitude of little known IQ societoes. The most famous high IQ society is Mensa, a society formed in Britain in 1946. The sole admission criteria to Mensa is an IQ score in the top 2% of the population. As explained above, the standard deviation of the IQ test in question is critical to making the determination of whether a particular IQ test scores qualifies for Mensa’s membership hurdle. The following high IQ societies have different thresholds for admission.

• Mensa: requires an IQ in the 98th percentile (top 2%) or an IQ score of 132
• EPL high IQ Society: requires an IQ in the 98th percentile (top 2%) or an IQ score of 132
• The Deep Brain high IQ society: requires an IQ in the 97th percentile – and IQ score of 131 (16 SD), and applicants also require a Masters degree
• The International High IQ Society: requires an IQ score in the 95th percentile (126 with 16 SD)
• Tensa: requires an IQ score of 121 (16 SD) which represents a score at the 90th percentile

High IQ societies normally accept IQ scores from a raft of recognized IQ tests including Weschler, Binet, Otis, Cattell and other Mensa-developed IQ tests such as the Wonderlic, the Matrix IQ tests, and the Figure Reasoning Test (FRT). Mensa also administers proctored IQ tests which means that the Mensa test can represent a wide variety of tests.

Take our culture fair IQ tests.