#### Table of Contents

### Introduction

The “unweighted” mean center is mainly used for events that occur at a place and time such as burglaries. The weighted center, however, is predominantly used for stationary features such as retail outlets or delineated areas for example (such as Census tracts). The *Weighted Mean Center* does not take into account distance between features in the dataset.

The weight needs to be a numerical attribute. The greater the value, the higher the weight for that feature.

Sources:

The Esri Guide to GIS Analysis, Volume 2: Spatial Measurements and Statistics.

An Introduction to Statistical Problem Solving in Geography

This course is designed to instill the basics of Python Programming by incrementally increasing your knowledge session-upon-session. In each section you will be given new material for a workbook to fill out and by the end of this course you will have your very own Python reference handbook. So how does this course have a GIS focus? Simple, most elements of the course have GIS and geospatial data in mind. Instead of using non-descript variables and values, we will use terms such as population, city, x_coord, y_coord, and so on. This will aid participants with pinpointing how they can relate geospatial data to Python.

### The Formula

The *Weighted Mean Center* is calculated by multiplying the x and y coordinate by the weight for that feature and summing all for both x and y individually, and then dividing this by the sum of all the weights.

For *Point* features the X and Y coordinates of each feature is used, for *Polygons* the centroid of each feature represents the X and Y coordinate to use, and for *Linear* features the mid-point of each line is used for the X and Y coordinate.

### Using GeoPandas to Calculate the Weighted Mean Center

The code below uses GeoPandas and Shapely to find the weighted mean center for a dataset based on the formula above and create an output file. In our example we will use a Shapefile, but you can use any input and output filetypes that you have available with your GeoPandas setup.

The code is heavily commented for ease of understanding the workflow. For a Point, we now we need get the mean value for all x values and y values. For a Polyline, we need to first get the midpoint of each line, and then get the mean value for all x values and y values for the midpoints. For a Polygon, we need to the the centroid value for each polygon, and then get the mean value for all x values and y values for the centroids.

` ````
```import geopandas as gpd
from shapely.geometry import Point
## input shapefile path
in_shp = r"path\to\input\shapefile\input.shp"
## the output shapefile path for the weighted mean center point
out_shp = r"path\to\output\shapefile\output.shp"
## the field that contains the numerical weight
weight_fld = "FIELD_NAME"
## read in the shapefile to a GeoDataFrame
gdf = gpd.read_file(in_shp)
## get the geometry type from the first record
geom_type = gdf.geom_type[0]
## get the EPSG code
crs = gdf.crs
## for Point geometry
if geom_type == "Point":
## get all x and y values
gdf["x"] = gdf.geometry.x
gdf["y"] = gdf.geometry.y
## for LineString geometry
elif geom_type == "LineString":
## get all x and y values for the midpoints
gdf["midpoint"] = gdf.geometry.interpolate(0.5, normalized=True)
gdf["x"] = gdf["midpoint"].x
gdf["y"] = gdf["midpoint"].y
## for Polygon geometry
elif geom_type == "Polygon":
## get all x and y values for the centroids
gdf["centroid"] = gdf.geometry.centroid
gdf["x"] = gdf["centroid"].x
gdf["y"] = gdf["centroid"].y
## get the sum of the x and y values multiplied by the weight for each feature
sum_of_x_wgts = (gdf["x"] * gdf[weight_fld]).sum()
sum_of_y_wgts = (gdf["y"] * gdf[weight_fld]).sum()
## get the total sum of all weights
sum_of_wgts = gdf[weight_fld].sum()
## divide the sum of x and y weights by the sum of the weights
weighted_x = sum_of_x_wgts / sum_of_wgts
weighted_y = sum_of_y_wgts / sum_of_wgts
## create a point geometry representing the weighted mean center
weighted_mean_center = Point(weighted_x, weighted_y)
## create a GeoDataFrame with the point geometry
gdf_weighted_mean_center = gpd.GeoDataFrame(geometry=[weighted_mean_center], crs=crs)
## add fields for the XCoord and YCoord
gdf_weighted_mean_center["XCoord"] = weighted_x
gdf_weighted_mean_center["YCoord"] = weighted_y
## write the weighted mean center point to the output shapefile
gdf_weighted_mean_center.to_file(out_shp, driver="ESRI Shapefile")

### Weighted Mean Center in Action

Data for Primary School location was downloaded from the Department of Education (Ireland) and processed to contain Primary Schools in County Kildare in a projected coordinate system – Irish Transverse Mercator (EPSG:2157). You can download the Shapefile containing the data used below here.

Running the script produces a Shapefile that contains the Weighted Mean Center based on schools in Kildare using the total number of pupils as the weight factor.

Below is a comparison between our GeoPandas tool and the (Weighted) Mean Center tool output from ArcGIS Pro. Spot on!

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### Also in this series...

- Mean Center
- Central Feature
- Median Center
- Standard Distance
- Weighted Central Feature
- Mean Center by Case
- Standard Distance by Case