So at its origins, IQ testing was used to weed out children with lower-than-average intelligence quotients, rather than to identify giftedness. The term IQ or intelligence quotient was truly descriptive of the process by which intelligence was ascertained. When Binet first developed his measurement technique, he set out to establish a scale of mental abilities (MAs) for children of different age groups. So in effect, he used tests of verbal ability to determine, on average, the proficiency level for children of each age group. Once it became clear of the range of performance outcomes that could be expected for children of a given age, he then compared this to the actual calendar age (CA) of the test taker. More specifically, IQ was calculated as MA/CA x 100. So if the child’s MA was equal than his or her CA, then that child have been considered to have an average IQ because MA=CA. Taking an example, a six year old with an MA of 6 would have an IQ of MA/CA x 100 = 6/6 x 100 = 100. This is exactly where the concept of average IQ being 100. In other words, average IQ means that your intellectual ability is commensurate to your age.

### Average IQ – the normal distribution

In the 1930s, Weschler introduced the concept of standard score which would eventually replace the MA/CA IQ measure. The benefit of using standard scores included that they were much more robust than the MA/CA technique which would break down for older test takers. It would then be established that IQ followed a normal distribution, with a mean (or average IQ) of 100 and a standard deviation corresponding to the observed distribution of variability of test responses by the individual test takers. With the mean and standard deviation known, then statisticians were able to compute test statistics and determine how individual test scores ranked relative to the average.

Assuming a standard deviation of 16 points, we know that c.68% of the population will have an IQ of between 84 and 116 points, and that 98% of the population will have an IQ which is two standard deviations from the mean, namely between 68 and 132. An IQ of 100 within a given country is assumed to the the average IQ level. However, clinical psychologists consider an IQ ranging between 90 and 109 to be average IQ, or average intellectual ability. Based on the statistical properties of the normal distribution, we know that roughly 47% of the population have an IQ within the average range.

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