By definition, about two out of every one hundred people meet the criteria for mental retardation. The definition of mental retardation is set so that on average, about 2.3 percent of the entire population will fit into it. This much of the condition is politically defined and arbitrary.
IQ test results of seventy (70) or below are rare by design. There are basic statistical reasons for why this is so.
If everyone took an IQ test and you lined up all their scores, there would be a wide variation in scores. This is called a 'distribution' of scores. The average score (the 'mean') is the score that is the smallest distance away from all the other scores in the distribution. The mean is a measure of 'central tendency' and helps you understand where the center point of your score distribution is located. The actual mean score may not have actually been observed - it may instead merely be an imaginary score which nevertheless is the smallest distance away from all the other real (observed) scores. The mean is not necessarily the most commonly observed score, (the 'modal' score), or located exactly in the middle of all the scores (the 'median' score).
Once you know the mean of your score distribution, it is important to know the standard deviation. The standard deviation is simply the average distance away from the mean that any given score happens to be.
When naturally occurring attributes such as IQ (or hat size, for that matter) are measured, their distribution tends to approximate a particular inverted 'U' shape, which is tall in the middle and shorter on the ends. For reasons having to do with the nature of random distribution in the universe, the inverted 'U' shape tends to approximate a theoretical mathematical curve known as the 'normal curve'. The more scores you put into the distribution you are measuring, the closer your observed distribution tends to take on the perfectly smooth shape of the normal curve. We don't know why this is so - we just note that this is how things work.
Normal curves have a special property in that the area under the normal curve is a representation of the probability (the chances or likelihood) of observing any given score within a normal shaped distribution. If we can find the area between an observed score and the average score, and compare that area to the total area under the curve, we can know how likely it is that our observed score might have occurred by chance. This tells us, in turn, how common or uncommon it is to see a score of a given magnitude.
Normal curves are never actually found in nature, just approximations of them are. However, since observable score distribution shapes do tend to approximate normal curve shapes, we can treat score distributions as though they were actually normally shaped.
IQ test scores are standardized, which means they are designed to have a mean score of 100 and a standard deviation of 15. We know that 68 percent of the area under the normal curve occurs within one standard deviation of the mean, plus and minus. Therefore, IQ scores falling between 85 and 115 are common, and observed about 68 percent of the time. About 95 percent of the area under the normal curve occurs between two standard deviations, plus and minus, so IQ scores falling between 70 and 130 might be observed by chance 95 percent of the time. If we look at the amount of area left under the curve after subtracting the area falling between two standard deviations plus and minus (ignoring the area representing scores greater than 130), we have only about 2.3 percent of the area left, which is also how common it is to find an IQ score of 70 or less by chance in the general population.
By definition, IQ scores must be 70 or less (two standard deviations below the mean of 100 or less) in order to qualify for a diagnosis of mental retardation. IQ scores of up to 75 can also be diagnosed as mental retardation, because the test does have some measurement error associated with it. When that is the case, adaptive deficits must also be present.
IQ tests are typically broken into two parts. One part measures verbal intelligence (ability with words) and the other part measures spatial intelligence (ability with movement and the manipulation of space). Verbal and spatial intelligence scores can vary widely across the population and even within an individual's test scores. One person might have low scores across the board, while another person might do fairly well on one test and completely fail at the other. Both people might have a low IQ score under 70, but their abilities would be very different; thus average IQ may be misleading when it comes to diagnosing mental retardation. In cases where a person's intellectual performance (as measured by the IQ test) is very uneven, diagnosticians tend to lean more heavily on separate tests of adaptive functioning in making the diagnosis of mental retardation.
