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.