Grading Size Variation

Calculate weighted population size CV and grading counts from weight/frequency observations; bins are left-closed at boundaries and no cannibalism threshold is inferred.

Description

Size variation in a counted fish sample is a frequency-weighted population CV.

Size variation in a counted fish sample is a frequency-weighted population CV. Grading boundaries divide the weight axis into bins, with each boundary belonging to the bin on its right.^[1]

Calculate weighted population size CV and grading counts from weight/frequency observations; bins are left-closed at boundaries and no cannibalism threshold is inferred.

When to use Grading Size Variation

Use this tool to calculate weighted population size CV and grading counts from weight/frequency observations; bins are left-closed at boundaries and no cannibalism threshold is inferred.

Prepare the cohort, water, feed or equipment measurements for one consistent operating period. Confirm nitrogen reporting bases, dry/wet masses, flow units and supplied design assumptions.

How to use Grading Size Variation and understand its results

Prepare the cohort, water, feed or equipment measurements for one consistent operating period. Confirm nitrogen reporting bases, dry/wet masses, flow units and supplied design assumptions.
Enter fishWeightsGrams, fishCounts, gradingBoundariesGrams using the field table and calculation rules, then run the tool.
Read weightedMeanGrams, populationCvPercent, gradeBinCounts. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
fishWeightsGrams	Fish weights grams	list of number	Required
fishCounts	Fish counts	list of number	Required
gradingBoundariesGrams	Grading boundaries grams	list of number	Required

Enter aligned positive weights and nonnegative integer frequencies with a positive total. Up to 127 positive strictly increasing grading boundaries define up to 128 bins; no boundaries means one bin. The tool computes weighted mean, population CV and weighted bin counts without expanding individual fish.

Paired lists must be nonempty and have equal lengths.

mean=Σweight×count/Σcount; CV%=100 sqrt(Σcount(weight−mean)²/Σcount)/mean

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
weightedMeanGrams	Weighted mean grams	number
populationCvPercent	Population cv percent	number
gradeBinCounts	Grade bin counts	list of number

json

{
  "input": {
    "fishWeightsGrams": [
      10,
      20,
      30
    ],
    "fishCounts": [
      1,
      2,
      1
    ],
    "gradingBoundariesGrams": [
      15,
      25
    ]
  },
  "output": {
    "weightedMeanGrams": 20,
    "populationCvPercent": 35.35533905932738,
    "gradeBinCounts": [
      1,
      2,
      1
    ]
  }
}

Limitations and assumptions

The SD uses the population denominator, not n−1. The output does not infer a cannibalism threshold or prove that a sampled distribution represents the full stock.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Grading Throughput: Plan batch grading duration with repeat passes, productive fraction and per-batch setup; reports unique fish throughput rather than counting repeated passes as new fish. For a complementary task, use Cannibalism Loss Estimate: Bound possible cannibalism losses using confirmed cases and unexplained missing inventory after other verified losses; does not assign unexplained losses to cannibalism.

References

Grading Size Variation — tool.io

Similar or alternative tools

Grading Throughput
Plan batch grading duration with repeat passes, productive fraction and per-batch setup; reports unique fish throughput rather than counting repeated passes as new fish.
Cannibalism Loss Estimate
Bound possible cannibalism losses using confirmed cases and unexplained missing inventory after other verified losses; does not assign unexplained losses to cannibalism.