Included in this tutorial:

the Mean Center tool, including parameters and options

Example 1: Unweighted Mean Center
Example 2: Weighted Mean Center

the Median Center tool, including parameters and options

Example 3: Unweighted Median Center

the Central Feature tool, including parameters and options

Example 4: Unweighted Central Feature

Software version in examples: ArcGIS Pro 3.0.0

Tutorial Data: The tutorial includes demonstration with sample data available here.

Credits: L. Meisterlin with Varisa Tanti and Nikolas Michael (2022)

This tutorial demonstrates three tools for finding the average center of a set of input features in ArcGIS Pro: the Mean Center, Median Center, and Central Feature tools.

The Mean Center Tool

Access the Mean Center tool by clicking the Geoprocessing toolbox in the main ribbon, and clicking through Spatial Analysis Tools > Measuring Geographic Distributions > Mean Center.

You can also search for ‘Mean Center’ in the search bar.

Mean Center Parameters & Options

In the Mean Center dialogue box, you will see these fields: Input Feature Class, Output Feature Class, Weighted Field, Case Field, and Dimension Field.

Here’s a brief description of the different inputs:

Input Feature Class: Specify the layer as your input feature class. The options that appear in the drop-down menu will be the layers currently in your map’s Contents. You can also choose to browse for an input file (by clicking the yellow folder icon)
Output Feature Class: Name and indicate the location of the output feature class.
Weighted Field (optional): The numeric field, from the input feature class’s attribute table, used to create a weighted mean center.
Case Field (optional): The Case Field option allows you to specify categories of your input dataset based on a field in the attribute table. This would produce points at the mean centers for each of the categorized set of input features.
Dimension Field (optional): This field takes a numeric field in the input feature class and computes the average for all the values in that field. The results are included in the output feature class.

Example 1: Unweighted Mean Center

The parameters of the tool with no weight specified. The output is the unweighted mean center point (green).

The following is an example of calculating an unweighted mean center. The tracts (geometry type: polygons) are the input feature class.

Examining the results

The output of the mean center tool is a feature class that appears in the Contents panel (and the map view). The layer contains one feature point (above in green), which identifies the geographic center for the polygons in the Tracts layer.

Its attribute table includes the feature’s x- and y- coordinates in the CRS of the input feature class.

Example 2: Weighted Mean Center

The parameters of the tool with a weight field specified. The output is the weighted mean center is a point (orange), compared the the unweighted mean center (green)

The following is an example of calculating a weighted mean center. The tracts (geometry type: polygons) are the input feature class. The field for the weight comes from the layer’s attribute table. Here, the weight is based on the area of the tract polygons.

Examining the results

Just like in the weighted mean center example, the unweighted mean center tool produces a feature class that contains one feature point (above in orange) located at the mean center of the weighted input features. The image above displays both the weighted (orange) and unweighted (green) outputs, showing that the weighted mean center of the input polygons is southeast of the unweighted mean center.

Its attribute table includes the x- and y- coordinates of the feature, in the CRS of the input feature class.

The Median Center Tool

Access the Median Center tool by clicking the Geoprocessing toolbox in the main ribbon, and clicking through Spatial Analysis Tools > Measuring Geographic Distributions > Median Center.

You can also search for ‘Median Center’ in the search bar.

Median Center Parameters & Options

In the Median Center dialogue box, you will see these fields: Input Feature Class, Output Feature Class, Weighted Field, Case Field, and Attribute Field.

The input parameters for the median center tool are very similar to those of the mean center tool. Here’s a brief description of the different inputs:

Input Feature Class: Specify the layer as your input feature class. The options that appear in the drop-down menu will be the layers currently in your map’s Contents. You can also choose to browse for an input file (by clicking the yellow folder icon).
Output Feature Class: Name and indicate the location of the output feature class.
Weighted Field (optional): The numeric field, from the input feature class’s attribute table, used to create a weighted median center.
Case Field (optional): The Case Field option allows you to specify categories of your input dataset based on a field in the attribute table. This would produce points at the median centers for each of the categorized set of input features.
Attribute Field (optional): The data median will be computed for all fields specified here.

Example 3: Unweighted Median Center

The parameters of the tool. The output is the median center point (yellow).

The following is an example of calculating an unweighted median center. The points are the input feature class.

Examining the results

The yellow point represents the median center resulting from the tool’s algorithm, which calculates Euclidean distance to and from the input features (here, the points) and the locations within the study area.

The output feature class contains a point feature (yellow) at the location with the smallest total distance from all the input features. The output attribute table includes the feature’s x- and y-coordinates in the CRS of the input feature class.

The Central Feature Tool

You can access the Mean Center tool by clicking the Geoprocessing toolbox in the main ribbon, and clicking through Spatial Analysis Tools > Measuring Geographic Distributions > Central Feature.

You can also search for “Central Feature” in the search bar.

Central Feature Parameters & Options

In the Central Feature dialogue box, you will see these fields: Input Feature Class, Output Feature Class, Distance Method, Weighted Field, Self Potential Weighted Field, and Case Field.

The Central Feature tool’s parameters are very similar to the tools reviewed above. Here’s a brief description of the different inputs:

Input Feature Class: Specify the layer as your input feature class. The options that appear in the drop-down menu will be the layers currently in your map’s Contents. You can also choose to browse for an input file (by clicking the yellow folder icon).
Output Feature Class: Name and indicate the location of the output feature class.
Distance Method: This input specifies how distance is calculated from each feature to neighboring features. There are two options in the drop-down menu: Euclidean (straight-line) and Manhattan (cardinal right-angles).
Weighted Field (optional): The numeric field, from the input feature class’s attribute table, used to find a weighted central feature.
Self Potential Weight Field (optional): The distance or weight between a feature and itself.
Case Field (optional): The Case Field option allows you to specify categories of your input dataset based on a field in the attribute table. This would find the central feature per group of categorized input features.

Example 4: Unweighted Central Feature

The parameters of the tool. The output is the central feature point (cyan).

The following is an example of calculating an unweighted central feature. The points are the input feature class and the Distance Method is Euclidean.

Examining the results

Unlike the other two tools, the output of the central feature operation will, by definition, be located at the same location as one of the input features (that feature being the most “central feature”).

The resulting feature class includes only one feature—the cyan point in our example. Its attribute table includes the feature’s x- and y-coordinates in the CRS of the input feature class.

Finding the (Average) Center of Features