Midpoint calculation methods
The midpoint in the online tool, Let's meet in the middle, is calculated by finding the center of gravity for the places in the addresses list.
Basically it involves converting the latitude and longitude for the addresses into 3-dimensional (x,y,z) coordinates, finding their average, then converting the average coordinate back into latitude and longitude. The result is the average location for the addresses. You can check out the math calculations for the center of gravity if you're interested.
Let's meet in the middleGeographic midpoint calculator