million inhabitants, even though these are vastly different geographic realities. Another source of interpretation error is that if a large district and a small district have the same value (and thus the same color), the larger one will naturally look like more. Other types of thematic maps, especially proportional symbols and cartograms, are designed to represent extensive variables and are generally preferred. A spatially intensive variable, also known as a field, statistical surface, or localized variable, represents a property that could be measured at any location (a point or small area, depending on its nature) in space, independent of any boundaries, although its variation over a district can be summarized as a single value. Common intensive variables include densities, proportions, rates of change, mean allotments (e.g., GDP per capita), and descriptive statistics (e.g., mean, median, standard deviation). Intensive variables are said to be distributive over space; for example, if the population density of the United Kingdom is 250 people per square kilometer, then it would be reasonable to estimate (in the absence of any other data) that the most likely (if not actually correct) density of each of the five constituent countries is also 250/km2. Traditionally in cartography, the predominant conceptual model for this kind of phenomenon has been the statistical surface, in which the variable is imagined as a third-dimension "height" above the two-dimensional space that varies continuously. In Geographic information science, the more common conceptualization is the field, adopted from Physics and usually modeled as a scalar function of location. Choropleth maps are better suited to intensive variables than extensive; if a map user sees the United Kingdom filled with a color for "100-200 people per square km," estimating that Wales and England may each have 100-200 people per square km may not be accurate, but it is possible and a reasonable estimate. Normalization Normalization is the technique of deriving a spatially intensive variable from one or more spatially extensive variables, so that it can be appropriately used in a choropleth map. It is similar, but not identical, to the technique of normalization or standardization in statistics. Typically, it is accomplished by computing the ratio between two spatially extensive variables. Although any such ratio will result in an intensive variable, only a few are especially meaningful and commonly used in choropleth maps: Density = total / area. Example: population density Proportion = subgroup total / grand total. Example: