The Human Development Index (HDI) is a composite index used to measure the overall development of a country. It focuses on three fundamental dimensions of human development:

• Life Expectancy at Birth: This measures the average number of years a newborn is expected to live if current mortality rates continue.
• Education: This is assessed using two indicators — mean years of schooling for adults aged 25 years or older and expected years of schooling for children of school-entering age.
• Gross National Income (GNI) per Capita: This reflects the living standards and income levels of the country's residents, adjusted for purchasing power parity.

In light of this, let's evaluate the options given in the question:

1. Life expectancy at birth
   : This is directly included in the HDI as it is a measure of health and longevity.
2. Infant mortality rate
   : Although an important health statistic, this is NOT directly included in the HDI calculations. Instead, HDI considers life expectancy at birth, which is an indirect indicator of overall population health, including infant mortality.
3. Mean years of schooling
   : This is a direct indicator used in the HDI to measure educational attainment.
4. Gross National Income per capita
   : This directly measures the standard of living and is included in the HDI.

Therefore, the correct answer is Infant mortality rate as it is not directly included in the Human Development Index calculation.