The document discusses the differences between calculating the mean center and median center of a dataset. It explains that the median center tool finds the point that minimizes the total distance to all features in the dataset using an iterative algorithm, making it less influenced by outliers than the mean center. It also describes how feature centroids are handled for different geometry types, and how the case field can be used to calculate median centers for separate groups. The output is a feature class containing the x and y coordinates of the median center(s) as attributes.

1. Can you please explain and solve #1? Thanks! 14 women delivering at a hospital on a single
day had made the following number of prenatal visits prior to their delivery. Show that is
centered at the median Show that is centered at the median
Solution
While the Mean_Center tool returns a point at the average X and average Y
coordinate for all feature centroids, the median center uses an iterative algorithm to find the point
that minimizes Euclidean distance to all features in the dataset. Both the Mean_Center and
Median Center are measures of central tendency. The algorithm for the Median Center tool is
less influenced by data outliers. Calculations based on feature distances require 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. The Case Field is used to group
features for separate median center computations. When a Case Field is specified, the input
features are first grouped according to case field values, and then a median center is calculated
for each group. The case field can be of integer, date, or string type, and will appear as an
attribute in the Output Feature Class. The x and y values for the median center feature(s) are
attributes in the output feature class. The values are stored in the fields XCOORD and
YCOORD. The data median will be computed for all fields specified in the Attribute Field(s)
parameter. 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.