The Summarize Center and Dispersion tool finds the central feature, central tendency, and standard deviational ellipse of a set of features.

The output is a hosted feature service that contains one to four feature layers.

## Examples

Example scenarios for using this tool include the following:

- A local government intends to open a new library for an underserved community. A GIS analyst identifies the block groups that have the appropriate zoning and uses the Central feature option of the tool to select the central block group that will best serve the community.
- A GIS analyst can compare the location of 911 calls to the locations of emergency response stations (for example, police, fire, and ambulance) using the Mean center option of the tool.
- A crime analyst wants to evaluate whether the median center of burglaries shifts between the daytime and nighttime. The analyst solves the problem by applying the Median center option of the tool and grouping the burglaries by the time of day.
- A GIS analyst for a non-governmental organization is analyzing the spread of an infectious disease. The analyst applies the Ellipse option of the tool and groups the features by week to evaluate how the disease is spreading.

## Usage notes

The Summarize Center and Dispersion tool includes configurations for input features, calculation settings, and the result layer.

### Input features

The Input features group includes the Input layer parameter, which specifies the point, line, or polygon layer for which the central feature, central tendency, or standard deviational ellipse will be determined.

### Calculation settings

The Calculation settings group includes the following parameters:

- Summary types specifies the methods that will summarize the center and dispersion of the features. Multiple methods can be selected. The following are the parameter options:
- Central feature determines the most centrally located feature by finding the feature that minimizes the Euclidean distance to all the other features.
- Mean center determines the mean center location by finding the geographic center of all the features. The geographic center is a point at the average x and y value of the input feature centroids.
- Median center determines the median center by finding the point that minimizes the Euclidean distance to all the other features. The median center is less influenced by data outliers than the mean center.
- Ellipse creates an elliptical polygon that summarizes the average location, dispersion, and orientation of the features. The center of the ellipse is at the mean center. The standard deviation of the x-coordinate and the y-coordinate from the mean center determines the axes of the ellipse. The angle, clockwise, between north and the long axis of the ellipse reflects the orientation of the features.

- Ellipse size specifies the size, in standard deviations, of the elliptical polygon. If distance between the mean center and feature locations follows a Rayleigh distribution, the 1 standard deviation, 2 standard deviations, and 3 standard deviations options will output an elliptical polygon that will cover 63 percent, 89 percent, and 99.9 percent of the features, respectively. This parameter is required when Summary types is set to Ellipse.
- Weight field specifies the field that will be used to determine the feature weights. Features with higher weights will have a greater impact on the methods selected for Summary types.
- Group by field specifies the field that will be used to group features together. Each Summary types option will be calculated for each group.

### Result layer

The Result layer group includes the following parameters:

- Output name determines the name of the layer that is created and added to the map. The name must be unique. If a layer with the same name already exists in your organization, the tool will fail and you will be prompted to use a different name.
- Save in folder specifies the name of a folder in My Content where the result will be saved.

## Environments

Analysis environment settings are additional parameters that affect a tool's results. You can access the tool's analysis environment settings from the Environment settings parameter group.

This tool honors the following analysis environments:

- Output coordinate system
- Processing extent
##### Note:

The default processing extent in Map Viewer is Full extent. This default is different from Map Viewer Classic in which Use current map extent is enabled by default.

## Outputs

The tool includes the following outputs:

- CentralFeatureLayer—A point, line, or polygon layer containing the central feature. If the Group by field parameter is specified, the layer will include the central feature of each group.
- MeanCenterLayer—A point layer in which the point represents the mean center location of all the features. If the Group by field parameter is specified, the layer will include a point at the mean center location of each group. The layer contains fields reporting the x-coordinate and y-coordinate of the mean center location.
- MedianCenterLayer—A point layer in which the point represents the median center of all the features. If the Group by field parameter is specified, the layer will include a point at the median center of each group. The layer contains fields reporting the x-coordinate and y-coordinate of the median center.
- EllipseLayer—A polygon layer in which the polygon is the standard deviational ellipse of all the features. The size of the ellipse will vary based on the value of the Ellipse size parameter. The layer contains fields showing the x-coordinate and y-coordinate of the mean center, x-standard distance, y-standard distance, and rotation of the ellipse.

## Licensing requirements

This tool requires the following licensing and configurations:

- Creator or GIS Professional user type
- Publisher or Administrator role, or an equivalent custom role

## Resources

To learn more, see the following resources:

- Summarize Center and Dispersion in ArcGIS REST API
- summarize_center_and_dispersion in ArcGIS API for Python
- Mean Center in ArcGIS Pro
- Median Center in ArcGIS Pro
- Central Feature in ArcGIS Pro
- Directional Distribution (Standard Deviational Ellipse) in ArcGIS Pro