A Statistical Classification on a Mixture Distribution of Intelligence Quotients and Severe Mental Retardation

Main content of this paper is to classify IQ individuals into two categories of normal and abnormal groups. It is too difficult to divide IQ individuals into two groups of normal IQ group and abnormal group because of sparse number of cases with mental retardation. Therefore, we examined a normality of 1673 IQ individuals, but a significant difference was noted for the IQ data. The lowest three mentally retarded cases of less than or equal to 59 IQ score were excluded, the IQ data then fitted to a normal distribution well. The critical value which minimizes the probability of classification is obtained on the basis on an approximate technique with regard to normality. An approximate probability of misclassification for individuals at random from mixture of two normal populations is 25.5%.