Distribution of Data - Spatial Mathematics: Theory and Practice through Mapping - page 181

such as buildings, highways, and power lines, but more important, the flying
debris from such damage can inflict further damage far from their source.

Consider the discussion earlier in this chapter about the density of tornadoes.
Pan and zoom the map to be centered on Goodland, Kansas. What would you
estimate the density to be in terms of tornadoes over the time period indi-
cated per 100 square miles (an area 10 miles × 10 miles)? What is the density
per square mile? If the number of tornadoes in your chosen 100 square mile
area is four tornadoes, the density is one tornado per 25 square miles. What is
the likelihood of a tornado in a single year in that 100 square mile area? Since
there were four tornadoes in 100 square miles over a 50-year time span, the
likelihood of a tornado in any single year is 4/50 = 0.08, or 8%. Now, pan and
zoom the map to be centered on Oklahoma City. What would you estimate
the density to be in terms of tornadoes over the time period indicated per
100 square miles (an area 10 miles × 10 miles)? Oklahoma City seems to have
had about 20 tornadoes in 100 square miles. What is the density per square
mile? The density is 20/100, or 1/5, or one tornado every five square miles.
What is the likelihood of a tornado in a single year in that 100 square mile
area? The likelihood of a tornado in a single year in that 100 square mile area
that includes Oklahoma City is 20/50, or 0.4, or 40%. Compare your Kansas
and Oklahoma measurements. This 40% likelihood is five times greater than
the sampled Kansas likelihood of 8%. Is there a location elsewhere in the
USA where the density is higher than central Oklahoma? Central Oklahoma
appears to be the area with the highest tornado density, but test areas in
Texas, Missouri, and Illinois as well, since these areas seem to be prime spots
for tornadoes.

We have been examining the distribution of data through attributes, proxim-
ity, density, and showing data as points, lines, and polygons, while touching
on the concepts of scale and data quality. In the next section, we will turn
our attention to other measures of distribution of data, including measures of
centrality.

8.6 Mean center and standard deviational ellipse

Many measures of spatial distributions exist that touch on the disciplines of
geography as well as mathematics. Buffering, as was discussed earlier in this
work, and tessellations, discussed in the last chapter, are two such measures.
Space in this topic does not permit due treatment of all these measures, but
two measures that are powerful and yet easy to understand are the concepts
of a mean center and a standard deviational ellipse. A mean geographic cen-
ter is the point representing the average x and y values for the input feature
centroids. The Mean Center is given as

Σ

i n

Σ

i n

x y

= 1 i = 1 i

x = , y =

n n