Description
Compute ratio of paired sums, retaining signed denominator totals and null at zero; differs from the mean of individual ratios.
A descriptive statistic depends on what is counted, how observations are weighted, and which reference or denominator is used. Removing observations differs from replacing them at cutoffs, and a ratio of totals differs from a mean of individual ratios. Keep those conventions and measurement units explicit when comparing results.
Compute ratio of paired sums, retaining signed denominator totals and null at zero; differs from the mean of individual ratios.
When to use this tool
Use this tool to compute ratio of paired sums, retaining signed denominator totals and null at zero; differs from the mean of individual ratios.
How to use the tool and how it works
- Enter numerators, denominators using the field definitions below.
- Run the operation. Correct input errors before interpreting an output.
- Read result.ratio, result.numerator, result.denominator. Use the ordering, boundary rules and absence conditions described below.
Sum the two aligned lists separately, return both sums, and divide their totals unless the denominator sum is zero, when ratio is null.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| numerators | Finite numerator observations aligned with denominators. | Dense list of at most 128 finite numbers; integer/shape constraints above also apply. |
| denominators | Finite denominator observations aligned with numerators. | Dense list of at most 128 finite numbers; integer/shape constraints above also apply. |
| Output field | Interpretation |
|---|---|
| result | Object containing the named fields below. |
| result.ratio | Ratio of the two list sums, or null when denominator sum is zero. |
| result.numerator | Sum of supplied numerators. |
| result.denominator | Sum of supplied denominators. |
{
"input": {
"numerators": [
2,
4
],
"denominators": [
1,
3
]
},
"output": {
"result": {
"ratio": 1.5,
"numerator": 6,
"denominator": 4
}
}
}Limitations and assumptions
- This differs from averaging individual ratios; denominator terms may cancel even when each is nonzero.
- Use consistent units within each measured list and its reference/cutoffs. Ratios carry numerator units divided by denominator units unless those units cancel. Ordinary floating-point arithmetic is used; input validation does not establish statistical suitability.
- Every declared top-level input field is required and unexpected fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and no larger in absolute magnitude than the safe-integer limit; operations returning exact large integers use decimal text. Positions are zero-based and spans end exclusively unless the operation explicitly states a different convention.
Alternative or Complementary methods
Check the descriptive convention and denominator before comparing results. Use a separate inferential model when you need uncertainty, significance, causal interpretation or population estimates.
References
-
Tool behavior and example: Ratio Of Sums — tool.io
Similar or alternative tools
- Mean Of Paired Ratios
Compute the mean of explicit paired finite ratios, rejecting any zero denominator rather than silently omitting undefined pairs; no ratio-of-sums substitution.
- Asymmetric Absolute Deviation Totals
Separate total absolute deviations below and above an explicit reference, retaining asymmetric loss evidence without estimating a distribution.