How to calculate the midpoint of several geolocations in python

Question

Is there's a library or a way to calculate the center point for several geolocations points? This is my list of geolocations based in New York and want to find the approximate midpoint geolocation

L = [
     (-74.2813611,40.8752222),
     (-73.4134167,40.7287778),
     (-74.3145014,40.9475244),
     (-74.2445833,40.6174444),
     (-74.4148889,40.7993333),
     (-73.7789256,40.6397511)
    ]

Answer 1

Based on: https://gist.github.com/tlhunter/0ea604b77775b3e7d7d25ea0f70a23eb

Assume you have a pandas DataFrame with latitude and longitude columns, the next code will return a dictionary with the mean coordinates.

import math

x = 0.0
y = 0.0
z = 0.0

for i, coord in coords_df.iterrows():
    latitude = math.radians(coord.latitude)
    longitude = math.radians(coord.longitude)

    x += math.cos(latitude) * math.cos(longitude)
    y += math.cos(latitude) * math.sin(longitude)
    z += math.sin(latitude)

total = len(coords_df)

x = x / total
y = y / total
z = z / total

central_longitude = math.atan2(y, x)
central_square_root = math.sqrt(x * x + y * y)
central_latitude = math.atan2(z, central_square_root)

mean_location = {
    'latitude': math.degrees(central_latitude),
    'longitude': math.degrees(central_longitude)
    }

Answer 2

Considering that you are using signed degrees format (more), simple averaging of latitude and longitudes would create problems for even small regions near to antimeridian (i.e. + or - 180-degree longitude) due to discontinuity of longitude value at this line (sudden jump between -180 to 180).

Consider two locations whose longitudes are -179 and 179, their mean would be 0, which is wrong.