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“pull” the mean center of population away from the more sparsely populated
northern sections of the state. However, a mean center of hard rock mines
in Michigan would lie to the north of the geographic center, reflecting the
historic concentration of iron and copper mining in the Upper Peninsula in
the northern part of the state.
Throughout this topic, we have emphasized the care that must be taken in
using and interpreting the results of spatial analysis. In the case of mean cen-
ters and standard deviational ellipses, the input polygons and therefore the
centroids of those polygons is important. Changing the input data alters the
position of the mean center. For example, if cities are used instead of counties
in computing the mean center of population for Michigan, the mean center
will be in a different location. Another important influence on the location of
the mean center and standard deviational ellipse is the map projection that
is chosen. Since the map projection affects the input and final position of the
mean center, an equal area projection is best.
In the next section, you have the opportunity to compute the mean center and
standard deviational ellipse yourself using a GIS.
8.7 Activities using mean center and standard deviational ellipse
8.7.1 Computing and analyzing mean center and standard
deviational ellipse using historical population data
In the activity earlier in this chapter using ArcGIS Online, you used a web-
based GIS to visualize spatial and temporal patterns of tornadoes. However,
the online platform lacked the statistical tools that allow for more rigor-
ous quantitative analysis. In the following activity, you will use ArcGIS for
Desktop, with its extensive geoprocessing and spatial statistics tools, to more
thoroughly investigate a data set. The data you will use is the list of the
world's 10 most populous cities at selected periods over the past 2000 years.
You will examine the pattern of the 10 most populous cities from the year 100
to the year 2005, noting the changes in spatial pattern and populations. Next,
you will predict the 10 most populous cities in 2050 based on the growth rates
of countries around the world. You will think critically about how population
figures were derived in ancient times and today.
To begin, download the data from the ArcLessons library, on: http://
edcommunity.esri.com/arclessons/lesson.cfm?id = 411. Open the .mxd (ArcMap
GIS project file, a map document) that is contained within the zip file. A map
showing the 10 most populous cities for each year from the year 100 to 2005
will be visible. Next, examine the geographic mean centers of the 10 most
populous cities for each year. The center represents the pencil point that
would balance the 10 most populous cities if the cities lay on a plane surface.
The mean centers are weighted by population, so the larger cities pull at the
mean center more than the smaller ones ( Figure 8.6 ).
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