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How To: Use the Jenks optimization method to determine natural breaks in ArcView legends

Procedure

Summary
Instructions provided describe the Jenks optimization method, used to determine natural breaks in Arcview legends.

Procedure
The Jenks optimization method is also known as the goodness of variance fit (GVF). It is used to minimize the squared deviations of the class means. Optimization is achieved when the quantity GVF is maximized:

1. Calculate the sum of squared deviations between classes (SDBC).

GVF = -------------------

2. Calculate the sum of squared deviations from the array mean (SDAM).

3. Subtract the SDBC from the SDAM (SDAM-SDBC). This equals the sum of the squared deviations from the class means (SDCM).

The method first specifies an arbitary grouping of the numeric data. SDAM is a constant and does not change unless the data changes. The mean of each class is computed and the SDCM is calculated. Observations are then moved from one class to another in an effort to reduce the sum of SDCM and therefore increase the GVF statistic. This process continues until the GVF value can no longer be increased.

Further Reading
Jenks, George F. 1967. "The Data Model Concept in Statistical Mapping", International Yearbook of Cartography 7: 186-190.

Any comprehensive documentation on Cartography and/or Cartographic Analysis