The center of world population (i.e. the location that has the the smallest possible sum of distances to every person on the planet) is somewhere in the region of the China / Kyrgyzstan / Kazakhstan border, close to Almaty, Kazakhstan.
Although the everchanging nature and distribution of populatuions means it is impossible to pinpoint with certainty the exact world center, we have estimated it using the location and populations of world cities as a proxy for the distribution of the global population. Using this method, the center of world population minimizes the average distance to any person on the planet to ~5,800km.
In the case of cities of at least 1 million, we found that Almaty in Kazakhstan had the smallest average distance to the world population of 5,810km (3,610 miles) and Santiago in Chile had the greatest average distance to the world population 14,063km (8,737 miles). This would arguably make Almaty the most central city in the world and Santiago the most remote.
Before getting into methodology, it may be helpful to size this question. The Earth has a circumference of 40,075km (24,901 miles) meaning that if everyone else relative to you stood on the exact opposite side of the planet, the average distance to everyone would be 20,038km (half the circumference). This provides a theoretical max of what this average could be. If the world comprised of two equal sized cities on opposite ends on the planet and you stood in one of them, the average would be half of that, or 10,019km (6,226 miles). This is also the average that would be expected if the world population was evenly dispersed on the surface of the Earth.
We calculated the above data by using the location and population of world cities as a proxy of how the worlds population is distributed. In total we mapped all cities with a population over 100k (over four thousand cities). We then population weighted the distance for each of those cities to every other city in our database to compute the average distance for each city. This analysis is therefore predicated on the assumption that the distribution of cities with over 100k people is a good proxy for the distribution of ALL people on the planet. While this may be debatable, we do not believe the actual number would be far off of our proxy.
While here, explore your city extremes.