One of several cartographic techniques for displaying a geographic distribution using area fills to represent values. The map's theme is a collection of shades, colors, or textures, each of which represents a particular value.

What makes a choropleth map different from its dasymetric and isopleth brothers? It's all in the data, what each value represents, and the assumptions made about the values. Data for most geographic distributions is collected by dividing the study area into collection units (frequently political units such as states or counties), and deriving a value for each collection unit.

The data could be quantitative data:

State      Population
---------- ----------
Alabama     4,464,356
Alaska        634,892
Arizona     5,307,331
Arkansas    2,692,090
California 34,501,130
...        ...

However, the data may be non-quantitative (also called "nominal" data):

State      Governor's Party Affiliation
---------- ----------------------------
Alabama    Republican 
Alaska     Republican
Arizona    Democratic
Arkansas   Republican
California Democratic (Quiet, you.)
...        ...

But when a cartographer is presented with a table like this, all he or she has is one piece of information about each collection unit. The best the cartographer can do is treat each collection unit as if it were homogenous. And that is precisely what a choropleth map is: Each collection unit is filled with a consistent shade, color, or texture, representing that one value, all the way to its borders.

Choropleth maps of nominal data are straightforward: Each value gets a particular fill. The United States map where each state is filled in red or blue is familiar to people who watch news coverage of United States election results. But most quantitative distributions are "volumetric", that is, they count the occurrences of some phenomenon (such as population) in all parts of the collection unit, and arrive at a total value for each unit. A map which assigns a shade to a volumetric data total is a map that lies. Why?

When a choropleth map is made for such a distribution, the cartographer spreads a shade over the entire collection area. In our example, Alabama has approximately the same population as Arizona. If we were to assign fills (say shades of blue) based upon the population total alone, we might well assign the same shade of blue to both states. But Arizona is much larger in area than Alabama, and in a map that filled Arizona and Alabama with the same shade, anyone who looked at the map would assume that Arizona has a far greater population than Alabama. The effect would be even more pronounced between Alaska and Maryland (which has three times Alaska's population but 1/50th its land area). There is one step necessary to represent the distribution correctly: divide each value by the collection unit's area:

State      Persons per square mile
---------- -----------------------
Alabama     87.6
Alaska       1.1
Arizona     45.2
Arkansas    51.3
California 217.2
...        ...

We can assign a shade to each population density value, and fill in each state with that shade.

As of this writing, a chropleth map showing population density by state appeared at http://quickfacts.census.gov/qfd/maps/thematic/PL0200000.html. An ASCII art example of a choropleth map appears in my writeup under dasymetric.

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