The Human Development Index (HDI) is a summary measure of human development. It measures the average achievements in a country in three basic dimensions of human development: a long and healthy life, access to knowledge and a decent standard of living. The HDI is the geometric mean of normalized indices measuring achievements in each dimension. The HDI is the geometric mean of the three dimension indices and embodies imperfect substitutability across all HDI dimensions. It thus addresses one of the most serious criticisms of the linear aggregation formula, which allowed for perfect substitution across dimensions. Some substitutability is inherent in the definition of any index that increases with the values of its components. Data sources: Life expectancy at birth: UNDESA; Mean years of schooling: Barro and Lee; Expected years of schooling: UNESCO Institute for Statistics; Gross national income (GNI) per capita: World Bank.