IQ-Brain Blog

# IQ scales – how do they work? (part III)

This is the third posting that investigates the question of IQ scales and their associated problems.

In my first posting here, I provide background on Binet’s invention of IQ scales and his proposed quotient for the measurement of intelligence: IQ = (MA/CA) x 100, where MA is the mental age of the test taker and CA is the calendar age of the test taker. The CA is easy to establish while the MA requires a scale of its own and a robust norming exercise to establish what the MA of different children pertaining to particular age groups should be.

I also provided an example here, of how Binet’s equation breaks down as the test taker gets older. And the very simple reason why this happens is that MA scale was built for children and might have been valid for teenagers up to 15/16 years in age (although the modern academic literature suggests that fluid intelligence peaks at the age of 25). Under Binet’s IQ calculation method, MA would be capped at 15/16 while CA would increase linearly with the age of the test taker. This ultimately means that the old quotient method was totally useless for calculating the IQ of adults.

So I ended up describing an example about a fictitious test taker name Jean-Pierre, who for argument’s sake, begins to experience a normal cognitive decline by the time he reaches 42 years of age. Binet’s IQ scale and equation would predict that Jean-Pierre, with an MA of 14, would have an IQ of 33 points, which is a level associated with mental retardation. In the absence of some serious illness, this score clearly does not make any sense.

The simple MA/CA formula ends up breaking down in late adolescence. It was Lewis Terman who recognized the problem of variability of IQ scores and in response proposed the use of standard scores in the 1920s. But as most industries and sectors, test publishers were averse to change which meant that several publishers including offspring of the Binet test continued employing the MA/CA equation for quite some time despite the mounting body of criticism associated with this equation and IQ scale methodology.

### IQ scales revolutionized by standard scores

The introduction of standard scores changed everything and for the better. The standard scores would mean that the IQ scale would change from an MA-centric one to the establishment of a distribution (i.e. mean or average and standard deviation) of the performance of people of a given age on the test. This is another way of stating that the MA calculation was expanded to reflect the IQ test performance of a particular cohort of test takers organised by age.

More importantly however, this resulted in much less variable IQ scores for the same person over time. Also, the properties of the normal distribution are such that if the mean and standard deviation are known, then one can extrapolate what the distribution of IQ scores might look like across a population, without needing to rely on CA and MA estimates for each test taker.

The norming process for such a test is quite different for the Binet IQ scales. The test publishers needs to find a representative sample of test takers withing their home country. Once the test is administered across the representative sample, the mean performance and standard deviation is established on the test.  With these two variables, we can extrapolate distribution of results which are assumed to be centered on a mean of 100.

You can take out IQ tests by clicking here.

# IQ scales – how do they work (part II)

In my last posting here, I explained the origins of IQ testing and how Alfred Binet proposed a beautifully simplistic equation for the measurement of intelligence:

IQ = (MA/CA) x 100

Where MA = test taker’s mental age

CA = test taker’s chronological or calendar age

We then discussed how establishing CA is easy. However, in arriving at an IQ scale, you first need to construct an IQ scale for MA. The derivation of an MA scale would involve putting large groups of Parisian children, organised by age, through a series of mental tasks there were believed to be associated with cognitive ability and intelligence.

There would clearly be some subjectivity in establishing what the average performance was for each age group, but if the sample was large enough and the test questions well crafted, it would become reasonably easy to establish questions that all the six year olds would be able to answer, but that only some of the five year olds would be able to answer, and so on and so forth.

To make the IQ scale and the MA scale valid however, one would need to recruit five year old children from all part of the country (not just Paris) if one were really to create an IQ scale that would be applicable to the whole of France. So what is emerging here is that although Binet’s contributions to the art of IQ testing were significant, his methods were imperfect. The first imperfection would be that Binet’s IQ scale would only really be applicable to Parisian children (rather than the French as a whole – as we know now that average IQ scores are higher in urban areas than they are in rural areas) and that the establishment of an MA scale contained some degree of subjectivity in establishing the cut-off success rates for different questions that should be achieved  by children of a particular age group.

But the real fatal flaw in Binet’s simple IQ equation is that it would end up breaking down as the test takers grew older.

Let’s look at an example:

If Jean-Pierre, a 10 year-old, was established to have a mental age (MA) of an average 12-year old, then Jean-Pierre’s IQ score would be calculated as follows:

Jean-Pierre IQ = (12/10) x 100 = 120

So Jean-Pierre, with an IQ of 120, would be bright for this age. Jean-Pierre was an intelligent 10 year old boy.

### Binet IQ Scales – the MA scale would become its own downfall

But what Binet and others would soon come to realize is that the MA ‘peaked’ at 15 or 16 years of age (although we now believe that fluid intelligence peaks closer to the age of 25), which creates a challenge in using the above-mentioned equation. This is a typical example of an IQ scale problem.

By the age of 20, Jean-Pierre may then have had the MA of a 16 year old (the peak MA). So his IQ would be calculated as follows:

= (16/20) x 100 = 80. So all of a sudden, Jean-Pierre’s IQ has dropped to 80 from 120. Did he really become less clever?

But even if you were to correct for this issue by assuming that Jean-Pierre had an MA corresponding to his own age, i.e. MA = CA = 20, then this implies that his IQ would still have decreased to 100. A drop of 20 points vis-a-vis his IQ result at the age of 10.

So what is going on? What is happening to the IQ scale?

Well the answer is simple. The Binet IQ equation and his scale seemed to apply relatively neatly for children, and perhaps even teenagers up until the ages 15 or 16. But the problem would be exacerbated as the test taker aged. And this IQ scale would totally break down for older test takers in their 20s and beyond.

If Jean-Pierre, by the age of 42, would have then seen his MA decline to match that of the average 14  year old, (as mental ability declines after our late 20s) then Jean-Pierre’s IQ would then be

IQ = (14/42) x 100 = 33, which most modern IQ scales would agree corresponds to severe mental retardation. In the absence of Jean-Pierre having acquired a illness of some description, this would clearly not make any sense.

I will continue explaining the move towards more modern standard scores in my next posting.

Meanwhile, you can try iq-brain.devv.website’s IQ tests here.

# IQ scales – how do they work? (Part I)

Intelligence Quotient (IQ) scales have changed over time. When IQ tests were invented by Frenchman Alfred Binet in the late 1800s. IQ scores at that time were based on the very simple concept of Mental Age (MA) and Calendar Age (CA). In fact, the origin of the term Intelligence Quotient lies in the calculation of the intelligence score which was calculated as someone’s Mental Age divided by that person’s Calendar Age. Expressed mathematically, we get the following quotient:

IQ = (MA / CA) x 100

The multiplication of the score by 100 would help facilitate the interpretation of the IQ scale in that the score is an integer rather than being a fraction. But let me park this point for a few moments.

What can be clearly seen from this IQ equation is that if MA = CA, then the IQ score will be 1 x 100 = 100. If MA on the other hand exceeds the denominator of the equation, the IQ score will exceed 100, while if the MA is lower than the CA, then that person’s IQ score will be less than 100. It’s as simple as that.

So what does this mean in plain English? This means that under the old method of calculating IQ, a person with a Mental Age is excess of his years, will have an IQ which is greater than 100. If on the other hand, that person’s Mental Age is less than that person’s Calendar Age, than this person will have an IQ of less than 100. And yes, you’ve guessed it, if CA and MA are equal, than this person will have an IQ of 100. Binet’s equation was beautifully simple, and establish someone’s Calendar Age is simple enough (you establish their birthday and then you can calculate age!), but how does one go about establishing what a person’s MA should be?

### IQ scales – it first started with establishing an MA scale

This is where the concept of IQ scales come in. More specifically, Binet had to establish an MA scale for each population of children of a certain age. That is, in establishing an IQ scale, Binet first had to determine how each age group would perform on specific mental tasks that were believed to be relevant to the idea of cognitive function. So Binet would have needed to establish a series of tasks and would have needed to see how ‘far’ children of a given age would have gotten on these tasks, and made a determination as to what the average expectation was for each age group.

I will leave you to digest the points that I have made so far: (1) Binet invented the IQ test in the late 1800s; (2) he proposed a beautifully simplistic formula cor calculating IQ = MA / CA x100; (3) establishing CA is simple, but MA requires having a scale for each age group. This involved testing a large sample of children of particular age groups to establish what the average performance at every age should be.

In my next posting, I will explain why although beautifully simplistic, this Intelligence Quotient method would end up breaking down and would be superseded by standard scores.

In the meantime, you can try our IQ test here.

# Stephen Hawking IQ

Stephen Hawking is an English theoretical physicist and cosmologist who is associated with the University of Cambridge. Hawking has published in numerous academic journals and is well known for his work on black holes and radiation.

Hawking is an Honorary Fellow of the Royal Society of Arts, and a recipient of the Presidential Medal of Freedom,  the highest civilian award in the United States. In other words, Hawkings is a really intelligent guy. But how intelligent is he really? Although Stephen Hawking does not have an IQ test scores on public record, several web sources quotes that his IQ would be around 160. Assuming a standard deviation of 16 on the IQ test, an IQ of 160 corresponds to a score which is in the 99.99th percentile, which means 1 in 11,307 people. Stephen Hawking IQ of 160 is certainly a genius-level IQ. It is widely accepted that IQs of over 140 are typically associated with geniuses. However, I have argued in previous postings that the term ‘genius IQ’ should definitely be more than just a high IQ score on an IQ test, but rather this designation should be accompanied by a level of achievement and accomplishments which match the designation. In the case of Hawing, this is certainly the case. His achievements certainly corroborate the fact that Stephen Hawking IQ of 160 should be classified as genius level IQ.

Although an IQ of 160 is definitely extremely high, it is not among the highest IQ in the world. To put this score into context, based on statistics, we can establish that 734 people in London would have an IQ score which is at this level. That is a lot of people. Other famous people with IQs of 160 would include Bill Gates and Dolph Lundgren.

### Stephen Hawking IQ – surpassed by many

Christopher Hirata, a US mathematician, is believed to have an IQ which is over 225, while Kim Ung Yong is believed to have an IQ of 220. Stephen Hawking IQ levels of 160 are impressive, but they are surpassed by plenty of big figures in the world of academia and science.

Have you ever wondered what your IQ is? If so, you can test your IQ scientifically and accurately here.

At iq-brain.devv.website. we test IQ up to 148. A perfect score on the test would likely mean that the test taker’s IQ is higher than 148, and may even place the test taker within reach of Stephen Hawking IQ.

# Picture IQ test

There are several different types of IQ tests on the web. A large proportion of them focus on riddles and general knowledge based written questions. These types of tests are not true intelligence tests because they tend to be based on knowledge and will be biased towards people who were educated in the language of the test. A picture IQ test, or often called a matrix test, is less likely to suffer from construction bias. Although some pictures have a cultural meaning, picture based IQ tests are much more likely to place people on a level playing field for the purpose of the test. Picture IQ tests tend to focus on logical reasoning (e.g find the missing sequence) and will be less likely to confer an advantage to any particular group of individuals. Picture IQ tests measure fluid intelligence, which is associated with the right hemisphere of the brain and its ability for ‘simultaneous processing’. Fluid intelligence, also known as (Gfis the purest form on intelligence and is analogous to the raw processing power of the brain.

### The origins of picture IQ tests

Although IQ tests were developed in the late 1890s by Frenchman Alfred Binet, the initial IQ tests were not used to assess giftedness or general intelligence, but were rather used to weed our underperforming children from Parisian classrooms. IQ testing to asses giftedness really took off during World War I, when the US army required a way of categorizing US army recruits. Robert Yerkes had developed a test known as the Army Alpha, which was a group administered crystallized IQ test which would serve to classify servicemen based on intellectual ability. However, Yerkes and Otis observed that many potential army recruits did not perform well on the Army Alpha because of their limited knowledge of the English language. As a result, people who did not perform well on the Army Alpha were then administered the Army Beta, which was effectively a picture IQ test which did not require any prior knowledge of the English language.

To this day the Otis-Alpha is still used to test general intelligence and is particularly popular in NYC for assessing gifted children.

Picture IQ tests, or matrix IQ tests are the best tools for measuring fluid intelligence. At iq-brain.devv.website, we have developed three picture-based, fluid IQ tests that among the most accurate on the Web. We are confident that scores achieved on our tests will yield comparable results to a group-administered IQ test such as those administered by high IQ societies such as Mensa.

# Brain test

There are many kinds of tests that you can put your brain through on the web. Each different test will evaluate a different aspect of the brain and its distinct cognitive abilities.

More often than not, a brain test is associated with intelligence testing or IQ testing. But what is an IQ test really? In simple terms, an IQ test is a standardized evaluation of the core cognitive abilities which are thought to make up general intelligence. Some of my readers may have heard the term multiple intelligence. Although this term sounds intuitive and clever – is it not true that some people are mathematically smart but may have no common sense or street smarts? – the term multiple intelligence is very simply a way of stating that overall intelligence (G) is made up of different “brain or cognitive skills”.

Before listing some of these core cognitive skills, it is important to distinguish between (1) learned brain test skills – or Crystallized Intelligence (Gc)  ; and (2) innate skills of the brain or Fluid intelligence (Gf). Crystallized intelligence relates to what the brain is able to learn, retain and apply in relevant situations over time. In other words, Gc  relates to what you are taught in school and further education in addition to what you teach yourself over your lifetime. Assuming that your brain is able to retain even a fraction of the information which it learns, it makes perfect sense to believe that all else being equal, people who pursue higher education for a longer period of time should have higher crystallized intelligence than say a higher school dropout who is not interested in reading. Fluid Intelligence, on the other hand, relates to your brain’s ability to solve novel problems (i.e. problems never seen before). Gf can almost be likened to raw processing power of the brain, as it represents the brain’s logical reasoning and creative responses to new stimuli and novel problems. So the idea of street smarts is really a combination of both fluid intelligence and crystallized intelligence, although fluid intelligence will prevail in ‘think fast – life or death situations”.

So let’s come back to the idea of a brain test. Most brain tests on the web are IQ tests of some description. Crystallized intelligence brain tests are normally rather meaningless because you end up testing acquired brain knowledge which is akin to comparing people’s level of education and whether or not some people are more intellectually inclined that others. That is to say, it would be normal to expect someone with two PhDs and who is also an avid reader of the Economist and the New Yorker to do better at the crystallized verbal IQ brain test than someone who graduated from straight As from high school and who is about to embark on a college degree (even if this high school graduate will go on to earn the exact same PhD as the person who already has it).

## Brain test of fluid intelligence

But a brain test based on fluid intelligence, on the other hand is much more interesting and relevant as it has been shown that fluid intelligence is not influenced by the level of education that you have. In other words, even though you may have just graduated from high school, you are on a level playing with someone who has a PhD when it comes to fluid intelligence. This is so because obtaining a PhD will not teach you how to respond on a fluid intelligence brain test, which means that people with higher education are not advantaged in a fluid IQ brain test. That said, all else being equal, people with higher fluid intelligence will be more likely to be able to go on and achieve greater things in higher education because their raw processing brain power will help them achieve more.

It’s important to note that even fluid IQ brain tests will test different brain skills including (1) short-term memory or Gsm; (2) visualization or Gv; (3) Processing speed or Gs. A fluid intelligence test is therefore in many ways a multiple intelligence test.

At iq-brain.com, we have developed one of the most reliable fluid IQ brain tests on the web. Your average score on all three of our scientifically validated IQ tests should correlate highly to an IQ score which you might obtain on a professionally-administered group IQ test.

Take our Brain Test HERE.

# IQ elite at iq-brain.devv.website

iq-brain.com has been online for just over four months now. We have had hundreds of test takers take our three scientifically validated IQ tests. So how are we doing? Are the results as we would have expected them to be?

At iq-brain.com, we are confident that if you score at least 132 on our three tests (i.e. 98th percentile), then you would stand a very strong chance of achieving a similar score on a Mensa-administered group IQ test. Mensa accepts candidates that are able to achieve an IQ score which is in the top 2% of the population, clearly representing an IQ elite.

Thus far, the highest IQ scores (certainly an IQ elite) have achieved IQ scores in excess of 140, (99.4% percentile) which should not only be sufficient to qualify for Mensa, but is most definitely commensurate with ‘genius level’ IQ. But we know that IQ scores not only change over time as we age, but can also vary depending on the mood, energy and mental state of the test taker on the day of the test; and of course the test in question. It is well known that a lack of sleep can shave off up to 10 IQ points. On this basis, it should come as no surprise that some studies have shown that the correlation between the same person’s IQ scores on different tests is only 0.95.

Unsurprisingly, the test at iq-brain.com with the highest score is the Culture fair test 1. This first test is free to start, which means that the test taker can take the test at no cost, before choosing whether or not he or she would like to pay to reveal the score. As such, it is possible that test takers who take the test twice before deciding to pay for their result may therefore be achieving over-inflated test scores. This is so because fluid intelligence represents one’s ability to solve novel IQ test questions and problems. So those test takers who are taking the test more than once before paying for their scores to be computed will not be receiving an accurate test result.

IQ tests 2 and 3 on the other hand, cannot be started without paying and further cannot be abandoned mid way while cancelling the scores. For this reason, IQ tests 2 and 3 are the most accurate in respect of evaluating the IQ elites and testing people’s fluid intelligence. The highest recorded score for test 2 is 140, which again is commensurate to a genius-level of IQ. Interestingly, the highest IQ test score recorded on our test 3 is 125. Test 3 is the most unique of the three tests and definitely novel, and thus perfectly conceived for testing fluid intelligence.

We are looking forward to seeing whether individuals are able of achieving a score of 132+ on our fluid IQ test 3. Coming back to our original question of how we are doing since the launch of iq-brain.com, we would now re-adjust our original assertion that achieving a score of 132+ on each of our tests means that the test taker might be able to achieve a similar score on a Mensa-administered test. Rather, we can now look back and state with confidence that if you are able to achieve an IQ score of 132 on tests 2 and 3, then you are highly likely to be able to qualify for Mensa, but you will most definitely be part of an IQ test elite with fluid intelligence inside the top 2% of the population.

To try our tests 2 and 3, you can access our members area for free here.

# IQ test scores

IQ test scores are meaningless without the accompanying standard deviation of the test in question. I will walk through an example to help you understand IQ test scores and percentiles. Most IQ tests are assumed to have an average score of 100 (or put differently, the test publishers will norm the IQ tests to have a mean of 100 within a given country). The standard deviation of the test can vary however. Most of the well-known tests typically have a standard deviation of either 15, 16 or 24 points although tests with a standard deviation of 15 and 16 points are the most commonly seen.

We know from properties of the standard normal distribution that 50% of the population will have a score that is lower than the mean of 100, while the other 50% will have an IQ which is greater than the mean. This observation is clearly seen when you think about a bell curve.

We know from statistical properties of the standard normal distribution that about 68% of all IQ observations will fall within 1 standard deviation of the mean,  95% of all observations will fall within two standard deviations of the mean and 99.7% of all observations would fall within 3 standard deviations of the mean.

### IQ test scores and percentiles – an example

So let’s contextualize this with an example. Suppose that I take a culture-fair IQ test with a standard deviation of 16 points. From the above-mentioned statistical properties of the standard normal deviation, we know that about 68% of the population should achieve IQ test scores between 84 and 116 points (i.e. the mean of 100 + or – 16), while just over 95% of the population would have IQ test scores between 68 and 132 (i.e. 100 + or –  2 x 16), and 99.7% of the population would score between 52 and 148. Put differently, most observations of the entire population of IQ test scores will be covered within 3 standard deviations of the mean (in this case 100 + or – 48 points * i.e. 16 x 3).

Although this is interesting to people who like statistics, IQ test scores are most interesting when converted into a percentile. A percentile provides a ranking of the score within the context of the population of test takers.

Suppose that on this culture-fair IQ test, I get a score of 117 points (IQ of 117). To understand the percentile, I will need a standard normal table (also known as a Z table). You can access a Z-table online for free here.

I  then need to convert my IQ score into a Z-score before I can work out the percentile. The Z-score can be calculated as follows: Z =(X – u) / SD. Where X is the test result (117 in this example), u = the average score of the entire population (100 for most IQ tests), and SD is the standard deviation of the test in question (SD=16 in this example).

The Z score for my theoretical test result is calculated as follows Z = (117 – 100) / 16 = 1.060

With this IQ test score of 117 now converted into a Z-score of 1.060, you can turn to the Wikipedia Z table and you start by looking up the first two digits of the Z score (in this case 1.060) in the vertical column of the table, and then following on the relevant row until you land in the cell which corresponds to the next two digits of the Z-score (in this case second and third decimals of  1.060). The Z-table percentage is 0.35543 (or about 35.5%). This percentage is the probability of the IQ score being between 100 and 117. However, to turn it into a percentile, we would need to add the left hand side of the Normal distribution. That is, we know that each tail of the bell curve accounts for 50% of the population, so given that 117 sits in the right half of the distribution (and we already worked out that 35.4% of the population have an IQ score between 100 and 117), we need to add the 50% of observations in the left tail – i.e. IQ test scores less than 100). Adding these two percentages gives 85.5%. In other words, about 85.5% of the population will obtain an IQ score which is 117 or less. This means that a score of 117 on an IQ test with a standard deviation of 16 points is better than roughly 85.5% of test takers for this test. Flipping it around, a score of 117 on this test would put my score in the top 14.5% of test takers (i.e. 100% minus the percentile of 85.5% = 14.5%).

If my IQ test score were 90 on the other hand, the Z-score would be calculated as follows: 90 – 100 / 16 = – 0.625. Looking at the Z table, in the column (remember that you are looking at the first two digits of the Z-score, in this case 0.625), and following the row for the last two digits (in this case the second and third decimals in 0.625). So the issue here is that we have a Z-score corresponding to a second decimal of 0.2 (i.e. 0.23237 or 23.2%) and a Z-score with a second decimal of 0.3 (i.e. 0.23565 or 23.6%), There is no percentage corresponding to second and third decimals of exactly 25. So the answer will be somewhere which is about half way between the two values, (i..e [0.23237 + 0.23565]/2 = 0.23401 or 23.4%).

Remember that the Z-score gives us the probability of observing a value which is between the mean (i.e. 100) and the score achieved (i.e. 90 in this case). So, the probability of observing an IQ between 90 and 100 is 23.4%, which means that an IQ of 90 is higher than about 26.6% of the population (i.e. 50% in the left hand tail of the bell  curve minus 23.4% = 26.6%). So an IQ score of 90 is said to be at the 26.6th percentile.

At iq-brain.com, we automatically calculate percentiles for your IQ test scores. Take the test here.

# IQ and height

A recent study has confirmed what was already previously known: on average, IQ and height are positive correlated. It is important to emphasize that correlation does not imply causation, but rather that ceteris paribus, groups of tall people will likely have an average IQ which is higher than similar sized groups comprising shorter people. The study by the world class universities of Edinburgh and University College London analyzed data from thousands of Scottish families over a six year period. Unlike previous studies about IQ and height, the researchers analyzed DNA markers of over 6,800 unrelated people. The study concluded that 70% of the variation in IQ was genetic while the remainder was down to environmental factors.

IQ and height may be correlated but explanatory factors are still poorly understood. Plenty of theories have been put forward including that height may be a marker of good nutrition, maternal stress and overall general mental and physical health. Other possible explanations include that increased height may be associated with larger brain size, which could in fact explain the general association in fairly simple and logical terms.

OK, IQ and height are correlated. So what? Well the real life implication of higher IQ are well known. Prior studies have suggested that height at the age of 18 is a predictor of subsequent scholarly performance.  And scholarly performance is related to graduated prospects and thus the ability to secure a better job. This may also provide an insight into previous studies that linked height to earnings potential throughout one’s lifetime. So as a group, you would expect taller people to do better relative to shorter people.

### IQ and height: people are getting taller

The good new for the human race is that people are getting taller – a lot taller. Over the last 150 years, it is believed that the average height of humans has increased by nearly 10 cm (4 inches) in industrialized nations. If people have been getting taller, and if brain size has in fact been keeping pace with the overall increase in human height, this could potentially explain the Flynn effect, which states that people in industrialized nations have been increasing their IQ scores at a rate of 3 points per decade in the United States and up to 6.7 points per decade in places like the Netherlands. Interestingly, the Netherlands happens to be the industrialized nation with the highest average height for both men (6ft and 0.5 inches) and women (5 ft 7 inches). This again could help explain why the Dutch collectively have an average IQ which is higher than other industrialized nations. At iq-brain.devv.website, we have been keeping track of how well people from certain countries have been doing on our test. It so happens that two of the people with the highest IQs happened to be Dutch. It would be interesting to understand whether they also happened to be tall.

But being tall is not all good news. Taller people have also been shown to live shorter lives on average, are known to be more prone to back problems and large body sizes create a headwind for hearts pumping blood. This illustrates that you just can’t have it all.

If you are interested in testing your IQ, you can do so here.

# Mensa IQ

Mensa is a high IQ organisation and probably the best known one globally. It was founded in England in 1946 and accepts people from all walks of life, with the single condition that they have an IQ in the top 2%. So Mensa IQ corresponds to the brightest 2%. Why 2%? The reality is that this is an arbitrary decision, although the decision to go with 2% clearly makes the admission process highly selective. When I was growing up, the average size of a primary school classroom was about 30 students. So assuming a normal distribution (which did not necessarily hold true in my classroom), this would have meant that maybe 1 pupil per class might have had a Mensa IQ level.

But when most people talk about IQ, they don’t usually refer to a percentage although they probably should. If someone asks: “what’s your IQ?”, the answer is rarely: “top 7%” or any other percentage. Instead, people who are brave enough to answer the question will typically say something like: “I have an IQ of 117”, or something to that effect.

However, it is important to understand basic principles of the standard normal distribution to be able to understand IQ and the interpretation of IQ scores. IQ follows a normal distribution with a mean which is usually 100. The normal distribution feature implies that 50% of the population will have a IQ which is greater than the average, while the other 50% of the population will have an IQ which is lower than the average. But each IQ test will have its own distribution and dispersion of results. The technical term for the dispersion of results is known as the standard deviation (SD). So each test will have its own standard deviation. The important point to note is that under a normal distribution, irrespective of what the actual standard deviation is, 68% of the population will have a score which is within one deviation the mean (mean of X + or – 1 SD). From this, we know that 32% of the population will have an IQ which is outside 1 SD of the mean. More specifically, 32/2 = 16% of the population will have an IQ which is lower than X – 1SD (i.e. the left hand tail in this example), while 16% will have an IQ which is greater than X + 1SD (i.e. the right hand side of the tail). Extending this example, we know from statistical properties that 95.4% of people have an IQ which is within 2SD of the mean – which implies that 4.6% of the population will have an IQ which is outside 2SD of the mean. Dividing 4.6% by two gives 2.3% in each tail. And this is the level required to be achieved by Mensa – the Mensa IQ.

### Mensa IQ: the top 2%

I’ve just explained the statistical properties of the normal distribution and how an IQ in the 2% of the right hand tail is one which is 2 standard deviations from the Mean. Coming back to the concept of an IQ score (rather than a percentage), then what is the level of Mensa IQ?

Well, this depends on the test in question. As explained, each test will have its own distribution and dispersion of results. The well known tests will be normally distributed although they may have different standard deviations. The most famous tests either have a standard deviation of 15 or 16 points. So assuming a mean score of 100, this means that an IQ in the top 2% of the population will be one which is at least 2 standard deviations greater than the mean score of 100. In other words, for most cases, Mensa IQ is either 130 (15 SD) or 132 (16 SD). However, there are some tests which have a standard deviation of 24 points (e.g. Cattell verbal scale). On this case, the qualifying Mensa IQ score would be 148 or higher.

Do you have what it takes to get into Mensa? Have a go at our Mensa-style practice tests here.