This study examines the relationship between a country’s human development index (HDI) and the number of societal offenders in jail (Off Index) for the country. Traditional analysis of this nature strongly veers towards linear (regression) analysis which may be inappropriate for the present case because of the high variabilities viz. fractality, of the data for the number of offenders in jails. The fractal correlation coefficient (fractogram) and the correlation of the fractal dimensions in tandem give a clearer picture of the degree of relationship induced by one highly variant variable on another variable than using the ordinary correlation coefficient. This is illustrated in the case of the relationship between the Human Development Index and the number of incarcerated offenders in the various countries of the world.