> 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)
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).
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.
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)