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There is a lot of speculation here on what this means, so I looked it up. The median center is the point through which a north-south and an east-west line each

by kens 3y ago

There is a lot of speculation here on what this means, so I looked it up. The median center is the point through which a north-south and an east-west line each divides the total population of the country in half. This is different from the "center of population", which is the balance point if you took an imaginary flat surface and put an identical weight on it for each person. These are both different from the geometric median. This document explains how the census bureau computed the values and has equations. There are complications since the earth is a sphere (as far as the census bureau is concerned): https://www2.census.gov/programs-surveys/decennial/2010/program-management/4-release/press-kit/center-of-population/centers-of-population-computation-documentation.pdf https://www2.census.gov/programs-surveys/decennial/2010/prog...

nonethewiser 3y ago
> which is the balance point if you took an imaginary flat surface and put an identical weight on it for each person. And with real weight for each person we'd see a center-point further south.
desertrider12 3y ago
> This is different from the "center of population", which is the balance point Does the difference only come from the earth curvature? I’m thinking if two lines each split the population in half, their unique intersection must also be the general balance point (for a flat surface anyway)
- function_seven 3y ago
  The balance point would rarely also be on the north-south, east-west intersection. The only time that would happen is if the distance of each person was also equal on either side of your meridian and your latitude. In reality, the clumpiness of the populations on either side of your dividing lines are going to be different. You could have a dispersed population on the west side of the meridian, but a concentrated population far away on the east side of the meridian.
- MathMonkeyMan 3y ago
  With center of gravity, adding a person far away from the center moves the center more than if you added them closer to the center.
- est31 3y ago
  Even in one dimension, the average and median don't have to be the same. In a list of numbers 1,2,3,4,100, the median is 3 but the average is 22. Same thing is done here, with same formulas to obtain them, just a two dimensional version (and some modifications to account for the meridians meeting at the poles, see the document linked by GP).

by kens 3y ago

nonethewiser 3y ago

> which is the balance point if you took an imaginary flat surface and put an identical weight on it for each person. And with real weight for each person we'd see a center-point further south.

desertrider12 3y ago

> This is different from the "center of population", which is the balance point Does the difference only come from the earth curvature? I’m thinking if two lines each split the population in half, their unique intersection must also be the general balance point (for a flat surface anyway)

function_seven 3y ago
The balance point would rarely also be on the north-south, east-west intersection. The only time that would happen is if the distance of each person was also equal on either side of your meridian and your latitude. In reality, the clumpiness of the populations on either side of your dividing lines are going to be different. You could have a dispersed population on the west side of the meridian, but a concentrated population far away on the east side of the meridian.
MathMonkeyMan 3y ago
With center of gravity, adding a person far away from the center moves the center more than if you added them closer to the center.
est31 3y ago
Even in one dimension, the average and median don't have to be the same. In a list of numbers 1,2,3,4,100, the median is 3 but the average is 22. Same thing is done here, with same formulas to obtain them, just a two dimensional version (and some modifications to account for the meridians meeting at the poles, see the document linked by GP).