In demographics, the center of population of a region is the geographical point nearest to all the inhabitants of that region, on average.
Centers of population are usually computed by minimizing a population-weighted average of a distance metric. In other words, for some place P, the distance from P to a list of populated places is computed, and the distance to each populated place from P is weighted by the population of that place. The choice of P for which such a weighted average has the lowest value is held to be the center of population for the particular list of populated places used.
In practice, the person or agency doing the calculation decides whether to represent the area of interest in two-dimensional or three-dimensional space, and also the specific function to use for computing distances. For the particular case of flat maps, the center of population could also be defined as a center of mass (centroid) of the population of the area of interest.
Decisions are also made on the granularity (i.e., the "coarseness") of the population data, depending on population density patterns or other factors. For instance, the center of population of all the cities in a country may be different from the center of population of all the states (or provinces, or other subdivisions) in the same country. Different methods may yield different results.
Practical uses for finding the center of population include locating possible sites for forward capitals, such as Brasilia, Astana or Austin. Practical selection of a new site for a capital is a complex problem that depends also on population density patterns and transportation networks.
It is important to use a culturally neutral method when dealing with the entire world. As described in
, the solution methodology deals only with the globe, and not with a two-dimensional projection of the Earth's surface. As a result, the answer is independent of which map projection is used or where it is centered. As described above, the exact location of the center of population will depend on both the granularity of the population data used, and the distance metric. With geodesic distances as the metric, and a granularity of , meaning that two population centers within 1000 km of each other are treated as part of a larger common population center of intermediate location, the world's center of population is found to lie "at the crossroads between China, India, Pakistan and Tajikistan", with an average distance of to all humans
The data used in the reference support this result to only a precision of a few hundred kilometers, hence the exact location is not known.
The mean center of United States population has progressed westward and, since 1930, southwesterly. This reflects the population drift over the last two centuries. The southwest drift reflects the rise of major populations across Texas, the exponential growth of Las Vegas, and the rise of Los Angeles, which became the second-largest American metro area, surpassing Chicago.
A median center of population can be used to show where the median east vs west person lives. A person living near Louisville, Kentucky has about half of the US population living north of him and half of the US population living south of him. This measure is meaningful only along the specific coordinate axes (north-south and east-west).
Recently, the Center for the Study of Global Christianity in Massachusetts declared that the world's Christian Center of Gravity was located in Timbuktu, Mali. According to their definition of Center of Gravity, half of all Christians live west of Timbuktu and half live south of Timbuktu. Presumably they had chosen the International Date Line to differentiate eastern from western people.