Does the distribution of IQs follow a bell curve?
The distribution of IQ test scores cannot be expected to follow a bell curve unless it is constructed by the tester to do so (Dorfman, 1978). The shape of the distribution of IQ test scores will depend on the average difficulty of the test items as well as their intercorrelations. The high item intercorrelations in IQ tests imply that the IQ distribution can take a variety of shapes. The central limit theorem does not apply to random variables with positive intercorrelations (Lamperti, 1966). Frederic Lord (1952), one of the fathers of modern test theory and former president of the Psychometric Society, gave results on this question: “The results given are sufficient to show that the distribution of test scores cannot in general be expected to be normal, or even approximately normal. The question naturally arises as to what possible shapes the frequency distribution fs, as given in (76) [Lord’s Equation (76)], may assume. The answer is that this function may assume any shape whatsoever
