This chapter discusses statistical maps which are used to display the distribution of a variable over a geographic area, usually defined by political boundaries. Topics covered include the selection of class intervals for the geographic area(s), shading, color, and legend to most effectively communicate the data. The chapter does not consider maps showing locations of geo-physical features (i.e., coal fields, crude streams) or diagrams of transportation networks (i.e., natural gas pipelines, coal slurries, shipping lanes) to be statistical maps.

In a statistical map, each unit (Petroleum Administration for Defense District, State, county, Census region, etc.) is illustrated by a shading pattern or color that represents the value (or range of values) for that unit of the variable. [30] The shading density or the color changes from one value or range of values to another value or range of values. This is illustrated in Figure 23.

The statistics shown on the map are expressed as rates, ratios, percentages, or other statistical measures and indices, not absolute numbers or totals. Yet, no matter what statistical measure or index is used, values in the distribution must be mutually exclusive and exhaustive.

Class Intervals
The first step in constructing a statistical map is to construct a frequency distribution of the data. (A histogram is a good method to use.) This is particularly important if the number of areas (i.e., States) is large. The frequency distribution is then divided into intervals. Ideally, the data will be grouped into four to eight class intervals, with each interval represented by the appropriate patterns, shading, or color.

Experience shows that spatial data do not necessarily conform to symmetrical bell-shaped curves. Many are multi-modal or skewed, or are U-shaped or J-shaped in various degrees. Intervals of equal size are desirable, but the character of many distributions makes this impossible. In the determination of class intervals, it is not an uncommon practice to rely on inspection to select natural divisions or breaking points in the distribution. Sometimes, a distribution is divided arbitrarily into a predetermined number of class intervals. Ideally, any technique for determining class intervals will minimize the differences within classes and maximize the differences between classes.

Shading and Color
The quality and scheme of shading or color on maps is of primary importance in making statistical maps an effective medium of visual communication. Plan shading and color schemes carefully, giving due consideration to the size or scale of the map, along with the amount of reproduction and reduction expected. A visual gradation in the shading or color from dense or dark to light is effective. The densest shading or darkest color (or hue) normally corresponds to the largest magnitude while the least dense shading or lightest color (or hue) normally corresponds to the smallest magnitude, with decreasing (or increasing) darkness or density showing the remaining range of categories.

The following are some helpful hints about using shading and color in statistical maps:

1. Try to keep the number of categories to a minimum to avoid using colors or shading that are so close to each other that even the most sharp-eyed reader would have trouble differentiating.
2. Make sure the same color is not used to portray both the categories of data and a geographic (i.e., lake or ocean) or other feature (i.e., borders) in the map. This can be confusing to readers and blur the clear presentation of the data.

The problems with color, to some extent, have been resolved by the introduction of color software with palettes that contain, sometimes, hundreds of colors; and hardware can sharply print many colors.

Legend
The ordering of colors or shading in a legend logically corresponds to the order of the range of values the coloring or shading represents, either from hight to low or vice versa.

Figure 23, which is based on graphs in EIA's report Electric Sales and Revenue 1989, DOE/EIA-0540(89), and updated with EIA's monthly report Electric Power Monthly shows average revenue per kilowatthour for electric utilities from the residential sector in each of the 50 States in 1991. The distribution of the data series is divided into four class intervals or categories: under 5.0 cents, 5.1 to 6.0 cents, 6.1 to 7.0 cents, and over 7.0 cents. Various colors represent the four categories.

Figure 23 shows regional patterns for the under-5-cents and over-7-cents-per-kilowatthour categories and random (dispersed over the country) patterns for the other two categories. The under-5-cents category pattern is the most pronounced. This category is comprised of two groupings of contiguous States: Washington, Oregon, Idaho, Montana, and Wyoming in the Northwest and Kentucky and West Virginia in the East.

There are several groupings of States in the over-7-cents-per-kilowatthour category. They are the New England and Middle Atlantic States, Michigan and Illinois in the Midwest, Florida in the South, New Mexico and Arizona in the Southwest, and the Pacific States of California, Alaska, and Hawaii. The United States average revenue per kilowatthour in 1991 was 6.7 cents.

Software permitting, authors could add (if they are not already on the map) the two-letter initials and the specific value for each State. Authors also could add, for example, a box with Census region or Census division averages.

Figure 23.

Average Revenue per Kilowatthour for Utilities, Residential Sector, by State, 1991

It is necessary to exercise care when using statistical maps to display data according to States or other political boundaries. As Tufte explains, "Maps have their flaws. They wrongly equate the visual importance of each country with its geographic area rather than with the number of people living in the country (or the number of cancer deaths). Our visual impression of the data is entangled with the circumstance of geographic boundaries, shapes, and areas". [31]

Maps are appropriate for weather measurements, such as State average rainfall per square mile, because large States do have more total rain than smaller States in the same rainfall category. Thus, area is proportional to the total rainfall. In the example above, revenue per kilowatthour is plotted and shows a tendency for contiguous States to have similar prices. It would not have been appropriate to plot total revenue for each State in this way.

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