Choropleth Class Break Quantiles Calculator
Type-7 linearly interpolated empirical quantile class boundaries; ties retained and no guaranteed equal member count.
Description
Generate type-7 empirical quantile boundaries from supplied observations.
Quantile map breaks mark fractions of a sorted observation distribution. Interpolating between adjacent observations creates numerical boundaries, but tied values can stop the resulting map classes from having equal counts.
When to use this tool
Generate type-7 empirical quantile boundaries from supplied observations. Use it when the input measurements and conventions below match the operation you need.
- Prepare observedValues, classes, respecting the measurement basis and boundaries below.
- Compare the worked example with your intended operation before reusing its result.
How to use the tool and how it works
- Enter every field in the input table using the stated units and exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
The tool sorts a nonempty observation list and evaluates type-7 empirical quantiles at j/classes, including zero and one. At fraction p it linearly interpolates at sorted position (n minus 1) times p. classes is an integer from 1 through min(128, n). tiesMayCollapseClasses is true when the number of distinct observations is smaller than classes.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| observedValues | Observed values. | List of finite numbers |
| classes | Classes. | Finite number |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.breaks | Breaks list, in the ordering described in the calculation. |
| result.tiesMayCollapseClasses | True when the distinct-value count is smaller than classes; this is a limited tie warning. |
{
"input": {
"observedValues": [
0,
10,
20,
30,
40
],
"classes": 2
},
"output": {
"result": {
"breaks": [
0,
20,
40
],
"tiesMayCollapseClasses": false
}
}
}Limitations and assumptions
- The tie flag is only the distinct-value comparison described above, not a complete class-assignment audit. Interpolated boundaries need not be observed values, and no tie-breaking assignment rule is applied.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
For a map-layout decision, inspect the rendered map at its intended size as well as its numerical dimensions. For classification or coordinate work, retain the chosen boundary and coordinate conventions with the result. Compare the scope of the nearby tools below before substituting one.
References
Similar or alternative tools
- Jenks Natural Breaks Simplified Classifier
Exact bounded one-dimensional dynamic-programming Jenks SSE partition, <=128 observations; deterministic earliest split ties, upper bounds may coincide.
- aspect octant classifier
Aspect Direction Octant Classifier from Slope Components: return downhill aspect, bearing degrees.