### Calculations

### Potential Applications:

- Mapping the distributional trend for a set of crimes might identify a relationship to particular physical features (a string of bars or restaurants, a particular boulevard, and so on).
- Mapping groundwater well samples for a particular contaminant might indicate how the toxin is spreading and, consequently, may be useful in deploying mitigation strategies.
- Comparing the size, shape, and overlap of ellipses for various racial or ethnic groups may provide insights regarding racial or ethnic segregation.
- Plotting ellipses for a disease outbreak over time may be used to model its spread.

### Output

The Distributional Trend tool creates a new feature class containing an elliptical polygon centered on the mean center for all features (or for all cases when a case field is provided). The attribute values for these output ellipse polygons include two standard distances (long and short axes), the orientation of the ellipse, and the case field, if specified. You can also specify the number of standard deviations to represent (1, 2, or 3). With features normally distributed around the mean center, one standard deviation (the default value) will cover approximately 68 percent of all input feature centroids. Three standard deviations will cover approximately 99 percent of all feature centroids.### Additional Resources:

Mitchell, Andy.*The ESRI Guide to GIS Analysis, Volume 2.*ESRI Press, 2005

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