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3.5 Interval Construction
The numeric intervals used for classifying and mapping rates are developed in four basic steps:
- The list of rates to be mapped is sorted into ascending order.
- The sorted list is compared to the number of intervals requested. If too many intervals have been requested, the number of intervals will be automatically reduced.
- The sorted list is segmented into approximately equal-sized groups, with the number of groups matching the requested (or reduced) number of intervals. Making all groups exactly the same size is usually not possible because the number of rates usually cannot be divided exactly by the number of intervals. The occurrence of ties, which are not divided across intervals, can also cause groups to be of different sizes.
- After the sorted rates have been divided into groups, the smallest rate and the largest rate in each group are identified. These are the initial endpoints for the intervals corresponding to the rate groups. These endpoints are then “bridged” so that any gaps between neighboring intervals are closed up. Bridging extends the initial endpoints to the midway point in each gap.
Once the intervals have been constructed, any unstable rates are reassigned to the special mapping category “Suppressed/Unstable/Undefined.” Reassignment of unstable rates is done after interval construction, to avoid biasing the interval endpoints. In some instances, an interval may lose all of its rates to this special mapping category.