Description
For integer count>=2 and 1<=firstRank<=lastRank<=count return midrank=(firstRank+lastRank)/2 and normalized=(midrank-1)/(count-1).
Normalization depends on the supplied center, scale, norm, range, reference distribution, or denominator. A zero spread and a missing denominator need an explicit policy, and clipping differs from fitting a scaler. Evaluating one scalar or derivative term does not estimate every parameter or establish a distributional improvement.
For integer count>=2 and 1<=firstRank<=lastRank<=count return midrank=(firstRank+lastRank)/2 and normalized=(midrank-1)/(count-1).
When to use this tool
Use Rank Normalization Single Tie Midpoint when you already have the required normalization parameters and need this local scalar, range, policy, or derivative term.
How to use the tool and how it works
- Enter firstRank, lastRank, count. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read midrank, normalized. Use the output convention below.
For integer count>=2 and 1<=firstRank<=lastRank<=count return midrank=(firstRank+lastRank)/2 and normalized=(midrank-1)/(count-1).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstRank | One-based first rank in the supplied tie group. | Required. Safe integer; minimum 1. |
| lastRank | One-based last rank in that group. | Required. Safe integer. |
| count | Count | Required. Safe integer; minimum 2. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| midrank | Midrank | Required. Finite number. |
| normalized | Scalar transformed under the stated formula and zero policy. | Required. Finite number. |
{
"input": {
"firstRank": 2,
"lastRank": 4,
"count": 5
},
"output": {
"midrank": 3,
"normalized": 0.5
}
}Limitations and assumptions
- Ranks are one-based and the output uses endpoint-inclusive rank normalization. The tie group and sample count are supplied; no sorting, rank assignment, or empirical percentile convention is inferred.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Fit or verify the intended scaler parameters and statistical model separately. Check units, zero policies, missingness, clipping, inverse conventions, and whether supplied norms or denominators belong to the same data.
References
Similar or alternative tools
- Percentile Scaler Explicit Cutpoint Gap
For lowerCutpoint<upperCutpoint return normalized=(value-lower)/(upper-lower), below=(value<lower), and above=(value>upper).
- Minmax Constant Column Output Policy
When equal, require value==minimum and return normalized=constantOutput and constant=true; otherwise return (value-minimum)/(maximum-minimum) and constant=false.