Mean Center (Spatial Statistics)


Identifies the geographic center (or the center of concentration) for a set of features.

Learn more about how Mean Center works


Mean Center illustration


  • The mean center is a point constructed from the average x, y and if available, z values for the input feature centroids.

  • This tool requires projected data to accurately measure distances.

  • The x, y and z values for the mean center point features are attributes in the Output Feature Class. The values are stored in the fields XCOORD, YCOORD and ZCOORD.

  • The Case Field is used to group features for separate mean center computations. When a Case Field is specified, the input features are first grouped according to case field values, and then a mean center is calculated for each group. The case field can be of integer, date, or string type. Records with NULL values for the Case Field will be excluded from analysis.

  • The Dimension Field is any numeric field in the input feature class. The Mean Center tool will compute the average for all values in that field and include the result in the output feature class.

  • This tool honors the 3D nature of your point data and will use x, y and z values in its calculations if z values are available. Since these results are 3D in nature, they will need to be visualized in a Scene. Be sure that you are running the analysis in a Scene or copy the result layer into a Scene for correct visualization of your analysis results.

  • For line and polygon features, feature centroids are used in distance computations. For multipoints, polylines, or polygons with multiple parts, the centroid is computed using the weighted mean center of all feature parts. The weighting for point features is 1, for line features is length, and for polygon features is area.

  • Map layers can be used to define the Input Feature Class. When using a layer with a selection, only the selected features are included in the analysis.

  • Caution:

    When using shapefiles, keep in mind that they cannot store null values. Tools or other procedures that create shapefiles from nonshapefile inputs may store or interpret null values as zero. In some cases, nulls are stored as very large negative values in shapefiles. This can lead to unexpected results. See Geoprocessing considerations for shapefile output for more information.


arcpy.stats.MeanCenter(Input_Feature_Class, Output_Feature_Class, {Weight_Field}, {Case_Field}, {Dimension_Field})
ParameterExplanationData Type

A feature class for which the mean center will be calculated.

Feature Layer

A point feature class that will contain the features representing the mean centers of the input feature class.

Feature Class

The numeric field used to create a weighted mean center.


Field used to group features for separate mean center calculations. The case field can be of integer, date, or string type.


A numeric field containing attribute values from which an average value will be calculated.


Code sample

MeanCenter Example (Python Window)

The following Python Window script demonstrates how to use the MeanCenter tool.

import arcpy
arcpy.env.workspace = r"C:\data"
arcpy.MeanCenter_stats("coffee_shops.shp", "coffee_MEANCENTER.shp", "NUM_EMP", "#", "#")
MeanCenter Example (Stand-alone Python script)

The following stand-alone Python script demonstrates how to use the MeanCenter tool.

# Measure geographic distribution characteristics of coffee house locations weighted by the number of employees
# Import system modules
import arcpy
# Local variables...
workspace = "C:/data"
input_FC = "coffee_shops.shp"
CF_output = "coffee_CENTRALFEATURE.shp"
MEAN_output = "coffee_MEANCENTER.shp"
MED_output = "coffee_MEDIANCENTER.shp"
weight_field = "NUM_EMP"
    # Set the workspace to avoid having to type out full path names
    arcpy.env.workspace = workspace
    # Process: Central Feature...
    arcpy.CentralFeature_stats(input_FC, CF_output, "Euclidean Distance", weight_field, "#", "#")
    # Process: Mean Center...
    arcpy.MeanCenter_stats(input_FC, MEAN_output, weight_field, "#", "#")

    # Process: Median Center...
    arcpy.MedianCenter_stats(input_FC, MED_output, weight_field, "#", "#")
    # If an error occurred when running the tool, print out the error message.


Output Coordinate System

Feature geometry is projected to the Output Coordinate System prior to analysis. All mathematical computations are based on the Output Coordinate System spatial reference.

Licensing information

  • Basic: Yes
  • Standard: Yes
  • Advanced: Yes

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