Geog 258: Maps and GIS

February 13, 2006 (Fri)

Quantitative thematic maps


Reading: chapter 7


Map symbolizations for quantitative thematic maps


Some map symbols have connotation of varying magnitude in value

Use them for representing the attribute measured in an ordinal, interval and ratio level



Measurement and count


How quantitative information is measured


Direct measurement from a zero-dimensional geographic feature (e.g. height of tree)

Use of data collection area: how many within the unit (e.g. census count)

Interpolation: inferred values from sample points (e.g. temperature)


Three spatial sampling methods


Measuring values at all locations are often infeasible

Appropriate sampling scheme needs to be employed


Random: arbitrarily sampled points

Systematic: gridded points

Stratified: make sure that certain characteristics of the population are adequately sampled


What is desirable sampling scheme?

As dense as possible in terms of random or systematic sampling

Be stratified in an appropriate (given applications) manner


Commonly used quantitative thematic maps


Proportional symbol map


varies map symbols in proportion to the magnitude


Map A                                     Map B                                     Map C


Difference between A and {B, C}?

Difference between B and C?


Proportional symbol map can use either pictographic or geometric element

Value can be measured either in continuous scale or be range-graded

Range-grading often adopts perceptual scaling to adjust for human eye’s underestimation of symbol size (in other words, the size of symbol is not exactly in proportion to magnitude in values of geographic features, but rather is slightly larger than their proportional values)


Proportional symbol map can be used for portraying point-like or line-like features; for example, line thickness or width is used to represent varying road class (which is ordered; see Figure 7.5)


Size of Shopping Mall


The location of symbol can be either at the actual location or in the representative location 


Dot map


This time, does not use size, use the number of dots to represent varying magnitude


How it is made?


Let’s say there are 10,000 people n in Pierce County

You decide unit value for each dot, let’s say 1000

The number of dots = total number of counts / unit value = 10,000 / 1000 = 10

As a result, 10 dots will be placed in Pierce County


How it works? I mean how people read/interpret this kind of map?


People usually do not count the number of dots, but rather attempt to gain a general impression of spatial distribution (how dense and how sparse)





Also the location of dots cannot be considered exact. Most of the time, it is randomly distributed within the observation unit (especially computer mapping). So what if the data is complied in the level of State? It is possible that many dots can be distributed in desert area, which does not provide fair representation of population distribution. Sometimes it is useful to adjust the distribution of dots to true variations given by related variables (e.g. land use).


Choropleth map


One of the most widely used thematic map

Due to prevalence of census data

Choro + pleth = area + value

Value applied to area


Values in area are shaded in varying tones of color (color hue or saturation)

As the value is measured in a ratio scale, a range of possible values are large.

It is common to group values into the limited number of class (classification)

The number of classes and classification methods have tremendous impact on appearance

Such decisions should be justified whenever appropriate (refer back to cartographic abstraction)



Can population density (normalized value) be seen as continuous phenomenon or discrete phenomenon? The value reported within the areal unit is presumed to be uniform. Tax rate per county? Representative value (e.g. median income, median age per census tract) is also seen as continuous statistical surface. If such values can be measured at all locations, it is considered continuous.


Isoline map


Shows continuous surface

Changes are gradual rather than abrupt

Usually made from interpolation of values at sampled points




Phenomenon space


Map types can be placed into two-dimensional matrix.


(1) Row: Discrete or continuous

Can values be measured at all locations?


(2) Column: Abrupt or smooth

Do values change abruptly or smoothly?






Proportional symbol map*

Dot map


Choropleth map

Isoline map


*when feature is at actual location

Other maps




Varies areal size in proportional to magnitude of values

It distorts geometry of real geographic features (e.g. political boundary), but sometime it can provide a fair portrayal of geographic phenomenon that you’re interested in because land size often overshadow our fair perception. Are you interested in candidate vote or land size?




Population map of the U.K.



Dasymetric maps


Shows variation within areas of inherent homogeneity

Small variation within area and large variation between areas



Compare cartogram/dasymetric maps to choropleth map


Cartogram vs. choropleth map: whether area size varies

Dasymetric vs. choropleth map:  the nature of boundary


Multivariate maps


Multiple variables can be mapped; good for showing related info (e.g. ethnic composition)



 use Chernoff’s method


Review questions


What type of map is this? {proportional symbol, dot, choropleth, isoline, cartogram, dasymetric}




What type of maps are these? {proportional symbol, dot, choropleth, isoline, cartogram, dasymetric}



What type of maps is this? {proportional symbol, dot, choropleth, isoline, cartogram, dasymetric}