generates equal ranges of value, but rather than starting with the minimum and maximum values, it starts at the arithmetic mean of the data and establishes a break at each multiple of a constant number of standard deviations above and below the mean. Quantiles divides the dataset so each class has an equal number of districts. For example, if the 3,141 counties of the United States were divided into four quantile classes (i.e., quartiles), then the first class would include the 785 poorest counties, then the next 785. Adjustments may need to be made when the number of districts does not divide evenly, or when identical values straddle the threshold. A Geometric progression rule divides the range of values so the ratio of thresholds is constant (rather than their interval as in an arithmetic progression). For example, the income range above would be divided using a ratio of 2 with thresholds at $40,000 and $80,000. This type of rule is commonly used when the frequency distribution of the data has a very high positive skew, especially if it is geometric or exponential. A nested means or Head/tail Breaks rule is an algorithm that recursively divides the data set by setting a threshold at the arithmetic mean, then subdividing each of the two created classes at their respective means, and so on. Thus, the number of classes is not arbitrary, but must be a power of two (2, 4, 8, etc.). It has been suggested that this also works well for highly skewed distributions. Because calculated thresholds can often be at precise values that are not easily interpretable by map readers (e.g., $74,326.9734), it is common to create a modified classification rule by rounding threshold values to a similar simple number. A common example is a modified geometric progression that subdivides powers of ten, such as [1, 2.5, 5, 10, 25, 50, 100, ...] or [1, 3, 10, 30, 100, ...]. Color progression The final element of a choropleth map is the set of colors used to represent the different values of the variable. There are a variety of different approaches to this task, but the primary principle is that any order in the variable (e.g., low to high quantitative values) should be reflected in the perceived order of the colors (e.g., light to dark), as this will allow map readers to intuitively make "more vs. less" judgements and see trends