A choropleth map (Greek choros-space & pleth-value) is a thematic map in which areas are shaded or patterned proportionally to the measurement of the statistical variable being displayed on the map. Examples of this are population density or per-capita income. Typically a color is associated with an attribute value, which is usually quantitative. Varying shades of color can then be used to visualize change in the attribute value. A choropleth map is an excellent way to visualize how a measurement varies across a geographic area and the level of variability within that area.
Choropleth maps are based on statistical data aggregated over previously defined regions (such as counties). Boundaries are not based off of the data value and are arbitary. In contrast, area-class and isarithmic maps use boundaries that are defined by the data. Therefore, where defined regions are important to a discussion (as in an election map divided by electoral regions), choropleth maps are preferred. When real-world patterns may not conform to the regions discussed because of issues like ecological fallacy and the modifiable areal unit problem (MAUP), other techniques are preferable.  For example, a map showing population may spread the color symbol representing Canada's population over its entire extent, while most of the population lies along the coasts and southern border of the country. Unfortunately, choropleth maps are frequently used in inappropriate applications due to the abundance of data and the ease of choropleth design using Geographic Information Systems.
When producing a choropleth map the cartographer must choose a graded color series or shades of grey to show least intense to most intense, a light to dark color pattern, to represent different classes of data being mapped. This helps group the data in organized ratio values. It is not advisable to use a rainbow color scheme in a choropleth map because each color has a different intensity and meaning, and might confuse the viwer as to what the data represents. Rainbow color schemes works better for nominal data.  The ColorBrewer, created by Cynthia Brewer of Pennsylvania, is useful in formulating color swatches for choropleth maps.
When the different areas being represented in a choropleth map are not all the same size, it is more appropriate to use density, ratios, or percentages rather than absolute values. For example, a map representing the overall population of the United States would look quite different than a map showing population density in the United States. In the first map, states with large populations, such as California, Texas, and New York, could be represented in a darker shade to indicate high population. However, when shown in the population density map, these states would not necessarily be shaded as darkly, because they are rather large states, allowing for smaller population per square mile. In the population density map, a much smaller state such as Connecticut could be shown in the darkest shade, because it is a small state, with less square miles for the population to fit within. Connecticut does not have a higher population than Texas or California, but has a much smaller land area, so the population density is much greater. 
The dasymetric technique can be thought of as a compromise approach in many situations. Broadly speaking, choropleth maps represent two types of data: spatially extensive data or spatially intensive data. Spatially extensive data are things like populations. The population of the UK might be 60 million, but it would not be accurate to cut the UK into two halves of equal area and say that the population of each half is 30 million. Spatially intensive data are things like rates, densities and proportions. These can be thought of conceptually as field data that is averaged over an area.
The earliest known choropleth map was created in 1826 by Baron Pierre Charles Dupin. 
The way data is classified and represented on a choropleth map determines how the data will be perceived and interpreted by the viewer. Choosing a classification method is an important decision because it will determinne how well the data are represented. Common classification methods include:
- Equal Interval: classification of data by making all class ranges equal but the number of observations per class may vary
- Quantile classification or Equal Frequency: classifying data by making the number of observations per class equal but varying the class ranges
- Arithmetic and Geometric Interval: used to classify data that replicated mathematical progressions
- Mean and Standard Deviations: can be used to classify data with a normal frequency distribution
- Nested Means: similar to Mean and Standard Deviations, but does not require a normal frequency distribution
- Natural Break Methods: grouping values by minimizing the within class variance but maximizes the between class variance; also called maximum homogeneity classification; uses traditional natural breaks or Jenks optimization
- User Defined: user creates own classification system if specific divisions are required
In mapping quantitative data, color progression will be used to depict the data meaningful way. Cartographers use many different types of color progression including single-hue, bi-polar, and qualitative progression.
Single-Hue progression fade from a dark shade of the color to a very light shade of the same hue color used. This is a common method used to show the magnitude of the data being represented on the map.
Bi-polar progressions are normally used with two opposite hues to show a change in value from negative to positive or on either side of a central tendency, such as the mean of the variable being mapped or other significant values like room temperature. For example a typical progression when mapping temperatures is from dark blue (for cold) to dark red (for hot) with white in the middle.
Qualitative progression is often used when working with nominal, characteristic, or qualitative data. It is when the colors shown on the map seem unrelated to one another, or are arbitrarily chosen. For example, on the map of the continental United States, shown on the right, the colors are arbitrarily chosen to represent the different states.
Choropleth maps can use random dots as an area symbol. They key difference between a choropleth map that with random dots and a dot-density map is the dispersion and purpose of the dots. In a choropleth map, the dots represent a quantity that is assumed to be constant throughout that polygon, and are randomly placed throughout the polygon. The individual placement of a dot in a choropleth map is not significant to the meaning of the map, but rather the dots as a whole within the polygon give meaning to the map. In a dot density map, the dots are used to show the geographic distribution and density of specific phenomenon within the polygon--each dot's placement within the polygon is significant. 
Choropleth Map Legend
The legend for a choropleth map is extremely important; without it, the classifications have no meaning. All map colors and symbols represent a value, which value is defined and explained in the map legend. The different values are represented in boxes within the legend and are usually listed vertically, but can be listed horizontally if the map is much wider than it is tall. 
Frequency Histogram Legend
The purpose of a frequency histogram legend in a choropleth map is to visualize statistical distribution and frequency counts in each class, in addition to serving as a key to the map. 
- T. Slocum, R. McMaster, F. Kessler, H. Howard (2009). Thematic Cartography and Geovisualization, Third Edn, pages 85-86. Pearson Prentice Hall: Upper Saddle River, NJ.
- “Choropleth Maps.” Illinois State http://my.ilstu.edu/~jrcarter/Geo204/Choro/Tom/. 22 Oct 2012.
- Tyner, Judith A.(2010), Principles of Map Design, The Guilford Press, New York, NY.
- Michael Friendly (2008). "Milestones in the history of thematic cartography, statistical graphics, and data visualization".
- Dent, B., Torguson, J., & Holder, T. 2009. Cartography: Thematic Map Design (6th Edition) [Chapter 6: Mapping Enumeration and Other Areally Aggregated Data: The Choropleth Map] Classification Method Compared pg. 108
- Kimerling, A Jon. "Dot maps vs. choropleth maps with random dot area symbols." ArcGIS Resources. 18 April, 2008. Web . 04 November 2013.
- Dent, B., Torguson, J., & Holder, T. 2009. Cartography: Thematic Map Design (6th Edition) [Chapter 6: Mapping Enumeration and Other Areally Aggregated Data: The Choropleth Map] Classification Method Compared pg. 111
- Kumar, N., Frequency Histogram Legend in the Choropleth Map: A Substitute to Traditional Legends. Cartography and Geographic Information Science. March, 2013
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- Business graphs and new data visualizations (including Choropleth map) inside Excel and PowerPoint
- MapsGeek An online free application to build and share thematic maps.
- StatPlanet - Free software for making interactive choropleth maps which can be published online or viewed offline.