Summary
Measures the degree to which features are concentrated or dispersed around the geometric mean center.
Illustration
Usage
The standard distance is a useful statistic as it provides a single summary measure of feature distribution around their center (similar to the way a standard deviation measures the distribution of data values around the statistical mean).
The Standard Distance tool creates a new feature class containing a circle polygon or sphere multipatch centered on the mean for each case. Each circle polygon or sphere multipatch is drawn with a radius equal to the standard distance. The attribute value for each circle polygon or sphere multipatch is its standard distance value.
This tool honors the 3D nature of your point data and will use x, y, and zvalues in its calculations if zvalues 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.
It is possible your 3D result may appear eggshaped instead of the expected sphere. The calculations, distances, and volumes are correct; however, the distortion is due to the zexaggeration when visualizing the result. You can adjust the Vertical Exaggeration on the Elevation tab of the Layer Properties window.
The Case Field parameter is used to group features prior to analysis. When a Case Field is specified, the input features are first grouped according to case field values. Then a standard distance circle is computed for each group. The case field can be of integer, date, or string type and will appear as an attribute in the Output Standard Distance Feature Class. Records with NULL values for the Case Field will be excluded from analysis.
The standard distance calculation can be based on the optional Weight Field parameter (to get the standard distance of businesses weighted by employees for example). The Weight Field should be numeric.
When the underlying spatial pattern of features is concentrated toward the center with fewer features toward the periphery (following a Rayleigh distribution), a one standard deviation Circle Size will cover approximately 63 percent of the features; a two standard deviations Circle Size will contain approximately 98 percent of the features; and a three standard deviations Circle Size will cover approximately 99 percent of the features in two dimensions. In three dimensions, a 6199100 percentage rule will result.
This tool requires projected data to accurately measure distances.

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.
Syntax
StandardDistance_stats (Input_Feature_Class, Output_Standard_Distance_Feature_Class, Circle_Size, {Weight_Field}, {Case_Field})
Parameter  Explanation  Data Type 
Input_Feature_Class  A feature class containing a distribution of features for which the standard distance will be calculated.  Feature Layer 
Output_Standard_Distance_Feature_Class  A polygon feature class that will contain a circle polygon for each input center. These circle polygons graphically portray the standard distance at each center point.  Feature Class 
Circle_Size  The size of output circles in standard deviations. The default circle size is 1; valid choices are 1, 2, or 3 standard deviations.
 String 
Weight_Field (Optional)  The numeric field used to weight locations according to their relative importance.  Field 
Case_Field (Optional)  Field used to group features for separate standard distance calculations. The case field can be of integer, date, or string type.  Field 
Code sample
The following Python window script demonstrates how to use the StandardDistance tool.
import arcpy
arcpy.env.workspace = r"C:\data"
arcpy.StandardDistance_stats("AutoTheft.shp", "auto_theft_SD.shp", "1_STANDARD_DEVIATION")
The following standalone Python script demonstrates how to use the StandardDistance tool.
# Measure the geographic distribution of auto thefts
# Import system modules
import arcpy
# Local variables...
workspace = "C:/data"
locations = "AutoTheft.shp"
links = "AutoTheft_links.shp"
standardDistance = "auto_theft_SD.shp"
stardardEllipse = "auto_theft_SE.shp"
linearDirectMean = "auto_theft_LDM.shp"
# Set the workspace (to avoid having to type in the full path to the data every time)
arcpy.env.workspace = workspace
# Process: Standard Distance of auto theft locations...
arcpy.StandardDistance_stats(locations, standardDistance, "1_STANDARD_DEVIATION")
# Process: Directional Distribution (Standard Deviational Ellipse) of auto theft locations...
arcpy.DirectionalDistribution_stats(locations, standardEllipse, "1_STANDARD_DEVIATION")
# Process: Linear Directional Mean of auto thefts...
arcpy.DirectionalMean_stats(links, linearDirectMean, "DIRECTION")
Environments
 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
 ArcGIS Desktop Basic: Yes
 ArcGIS Desktop Standard: Yes
 ArcGIS Desktop Advanced: Yes