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Introducing Geographic Information Systems with ArcGIS: A Workbook Approach to Learning GIS, 3rd Edition by Michael D. Kennedy

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Natural Breaks5
To understand “natural breaks” (also known as the Jenks method), you need to comprehend the idea of “variance from a mean.” If you have a cluster of values, they have a mean, or average, value. If you take each value and subtract the mean from it, you get another set of numbers. The variance used by the Jenks approach is calculated by squaring each of these new numbers, taking their sum, and dividing by the number of numbers. You can see that the variance would be larger the further the original values were from the mean. So the variance is an indication of the dispersal from the mean of the set of values. If we had, say, five clusters of numbers, each with its own variance, we could add those five variances together to get a total variance. The idea behind the Jenks approach is to minimize the total variance by moving values around from cluster to cluster. At the end of the process, it should be the case that no value can be moved from one class to another without raising the total variance. This method works so well that it is the default that ArcMap uses. It is illustrated by using a different data set.
____ 17. In Layer Properties > Labels, change Label Field to WOMBATS (click Apply) and, under the Symbology tab change Value Field to WOMBATS. Change the Show box to Categories–Unique Values. Click Add All Values. (Make sure WOMBATS is chosen in the Value Field) Click Apply, then click OK. Look at the quilt. Open the attribute table and sort the WOMBATS field ...

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