For example, in calculating the indices 39 and 70 for the frequency of retardation among ordinary delinquent boys as compared with elementary school boys, the percentages retarded at each life-age for each of these groups was multiplied by the number of ordinary delinquent boys at this age, as shown lower in the table, and the totals divided by the number of ordinary delinquents, 213. The average frequency of the retardation of a school group which compares in ages with the delinquent group was thus determined. In calculating the indices of amount of retardation the same procedure is followed except that the average number of years retarded is found for each age and this is multiplied by the number of delinquents at that age. The 16-year-olds are omitted because of the inadequacy of the school census for this age. According to the standard which regards 7 years as satisfactory in the first grade there can be no retardation under eight years of age. Since some of the pupils 13 years of age and over have reached high school and so do not show in the Minneapolis table the percentage of retardation for children 13-15 years is based on the assumption that the number of children at these ages will be the same as the average number for 11 and 12 years. No credit could be allowed for those advanced in school positions on account of the incompleteness of the Minneapolis census for older ages. The comparison is, therefore, on the basis of retardation alone. TABLE XIV. INDICES OF FREQUENCY AND AMOUNT OF SCHOOL RETARDATION OF MINNEAPOLIS JUVENILE DELINQUENTS COMPARED WITH MINNEAPOLIS SCHOOL CHILDREN OF CORRESPONDING AGES. (_Age 7 or younger regarded as satisfactory in the first grade._)