What are the ways to identify the center point in a cluster of point features?

Answer

Unlike identifying the centroid of a single feature, users may have data containing a cluster of point features and need to identify the center point in the cluster.

Note:
For more information on finding the centroid of a single feature, see the following articles: How To: Calculate feature centroids, and How To: Find the centroid of polygons using Calculate Geometry.

There are three tools that can be used to identify the center point in a cluster of points.

1. Central Feature
   
   The Central Feature tool identifies the most centrally located feature by calculating the distance from each feature centroid to every other feature centroid in the dataset. The feature with the shortest accumulative distance to all other features is selected as the central feature class. The Central Feature tool is useful for finding the feature with the smallest distance to all other features.
    
   
   
    
2. Mean Center
   
   The Mean Center tool finds the center feature from the average x- and y-coordinate of all the features in the study area. The Mean Center tool can be used to find the mean center based on different groups of features within the feature class, which allows users to make comparisons of mean centers between groups of features.
    
   
   
    
3. Median Center
   
   The Median Center tool is a measure of central tendency. Features can be assigned to a weight as the number of trips associated with each feature and the weighted median center is the location that minimizes the distance for all trips. The Median Center tool is useful when users want to find the central feature without being influenced by any outlying feature away from the cluster with a lower weight value than the rest.