168 sYMBOLizaTiOn
which is rare for geographic distributions. Standard deviation is a measure of disper-
sion; it is a way of stating how far the observations vary from the mean. It is defined
as the square root of the arithmetic mean of the squared deviations from the mean.
The boundaries of the class intervals are found by adding or subtracting the standard
deviation.
Quantiles are categories that contain an equal
number of enumeration areas
(observations) in each (Figure 8.29). If the areas involved vary widely in size, quan-
tiles may be misleading.
An
arithmetic progression is a sequence of numbers in which each term after the
first is determined from the preceding one by adding to it a fixed number called the
common difference, for example 2; 2 + 1,000; 1,002 + 1,000; 2,002 + 1,000; and so
on. The common difference here is 1,000. If the distribution graph approximates that
of an arithmetic progression, then it is possible to use this as the basis for categories
(Figure 8.30).
Geometric progression is a sequence of numbers in which each term after the
first is determined by multiplying the preceding term by a fixed number called a
com-
mon ratio (Figure 8.31). If 2 is again the first term and the ratio is 10, the progression
is 2, 2(10), 2(10)
2
, 2(10)
3
, or 2, 20, 200, 2,000, and so on.
Natural breaks are a graphic way of determining categories by examining the
data or the histogram and looking for breaks in the frequencies or change of slope
in graphs. This results in a natural grouping of similar values (Figure 8.32). This
method is often used by teachers in assigning student grades. For mapping it can pro-
duce categories that are very close to the data model.
Arizona
Population
Density
2000
4.4-86.7
86.8-169
169.1-251.3
251.4-333.8
fIgURe 8.28.
Choropleth map using equal steps.
Designing and Choosing symbols 169
