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GE 2110
Spatial Descriptive Statistics
 Descriptive measures of spatial data are important in
understanding and evaluating such fundamental
geographic concepts  accessibility and dispersion
 E.g. it is important to locate public facilities so that they
are accessible to defined populations
 Spatial measures of centrality applied to the location of
individuals in the population will result in geographic
locations that are in some sense optimal with respect to
accessibility to the facility
Zakaria Khamis
Spatial Descriptive Statistics
 Similarly, it is important to characterize the
dispersion of events around a point
 It is useful to summarize the spatial location of
individuals around a hazardous waste site
 Are the individual with a particular disease less
dispersed around the site than are people without
the disease? If so, this could indicate that there is
increased risk of disease at location near the site
Mean Center
 This is the most common used spatial measure of
central tendency
 For point data, x and y coordinates of the mean
center are found by simply finding the mean of the x
coordinates and the mean of y coordinates
 For areal data, the mean center can be found by
using the centroids of each area. It is often useful to
attach weights to the x and y coordinates
Mean Center
 For instance, to find the center a population, the
weights are taken as the number of people living in
each subregion
 The weighted mean of x coordinates and y
coordinates then provides the location of the mean
center of population
wi xi
wi yi
x  i 1n
y  i 1n
 wi
 wi
i 1
i 1
Mean Center
 Where the wi are the weights (e.g. population in
region i) and xi and yi are the coordinates of the
centroid in region i
 Conceptually, this is identical to assume that all
individuals living in a particular sub-region live at a
pre-specified point  centroid
 E.g. the mean center of population in the USA has
migrated west and south over time
Standard Distance
 Aspatial measures of variability, such as variance and
standard deviation, characterize the amount of
dispersion of data points around the mean
 Similarly, the spatial variability of locations around a
fixed central location may be summarized
 The standard distance is defined as the square root
of the average squared distance of points to the mean
center (Bachi 1963)
Standard Distance
sd 
i 1
 Where dic is the distance from point i to the mean
 The square root can be taken out from the equation
because, distance is absolute