The Problem column in the June 2012 issue of RSS News asked a good question. Where on the surface of the Earth is the point such that, if every person in the world were to travel directly to that location — as the crow flies — the total distance travelled would be minimised?
The answer is the demographic centroid of the world.1 The co-ordinates of that point are the weighted means of the co-ordinates of latitude and longitude of the centres of representative geographical areas (not necessarily of equal size). The weights are the populations of those areas.
Published estimates of the populations of 228 individual countries2 add up to 6,899,086,903. (Global estimates now put the entire population of the world at over 7,000,000,000.)
The US Board of Geographic Names has listed the latitudes and longitudes of the centres of those countries.3 Convert the fractional parts of the angular values to decimal format. Assign negative values to all Southern latitudes and to all Western longitudes.
The point 23°40′N, 50°59′E is the demographic centroid of the earth. It is situated in the eastern part of the Empty Quarter (in Saudi Arabia), almost directly on the Tropic of Cancer.
The antipodal point4 (at 23°40′S, 129°01′W) is located in the South Pacific near Pitcairn Island. It corresponds to the most distant point from everyone on Earth.
Multiply the standard deviations of the latitudes and longitudes of the centres of the countries by the square root of the sum of squares of the weights (where the sum of the weights equals unity).5
The results are estimates of the standard deviations of the latitude and longitude of the centroid (and also of its antipode). They are ±07°00′.and ±20°39′, respectively.a
On average, each person on the planet would travel a distanceb of 5,542 kmc to get to the demographic centroid. This distance has a standard deviation of plus-or-minus 1,206 kmd.
Each person on Earth would travel an average of 14,458 kmc to get to the antipode of the centroid. That distance has a stand-ard deviation of minus-or-plus 1,206 kmd.
From the global to a local level
The demographic centroid is a useful concept with which to analyse population movements over time in a given area.
The demographic centroid of the Republic of Ireland has meandered steadily eastwards over a cumulative distance of about 24 kilometres in the 85 years since 1926. That equals about 300 metres per annum. The average length of this shift from once census to the next was about one mile.
A decreasing logarithmic model accounts for three quarters of the variation in the shift over time.