is performed by establishing a classification rule, a series of thresholds that partitions the quantitative range of variable values into a series of ordered classes. For example, if a dataset of annual Median income by U.S. county includes values between US$20,000 and $150,000, it could be broken into three classes at thresholds of $45,000 and $83,000. To avoid confusion, any classification rule should be mutually exclusive and collectively exhaustive, meaning that any possible value falls into exactly one class. For example, if a rule establishes a threshold at the value 6.5, it needs to be clear about whether a district with a value of exactly 6.5 will be classified into the lower or upper class (i.e., whether the definition of the lower class is <6.5 or ≤6.5 and whether the upper class is >6.5 or ≥6.5). A variety of types of classification rules have been developed for choropleth maps: Exogenous rules import thresholds without regard for patterns in the data at hand. Established rules are those already in common use due to past scientific research or official policy. An example would be using government tax brackets or a standard Poverty threshold when classifying income levels. Ad hoc or Common sense strategies are essentially invented by the cartographer using thresholds that have some intuitive sense. An example would be classifying incomes according to what the cartographer believes to be "rich," "middle class," and "poor." These strategies are generally not advised unless all other methods are not feasible. Endogenous rules are based on patterns in the dataset itself. Natural breaks rules look for natural clusters in the data, in which large numbers of districts have similar values with large gaps between them. If this is the case, such clusters are probably geographically meaningful. The Jenks natural breaks optimization is a heuristic algorithm for automatically identifying such clusters if they exist; it is essentially a one-dimensional form of the k-means clustering algorithm. If natural clusters do not exist, the breaks it generates are often recognized as a good compromise between the other methods, and it is commonly the default classifier used in GIS software. Equal intervals or an arithmetic progression divides the range of values so that each class has an equal range of values: (max - min)/n. For example, the income range above ($20,000 - $150,000) would be divided into four classes at $52,500, $85,000, and $117,500. A standard deviation rule also