@plotnerd/stat-engine

Multi-algorithm quartile & statistics engine — the calculation core behind PlotNerd.com.

Calculate quartiles using five different algorithms in a single call. Compare results, get smart recommendations, and generate verification code for R, Python, Excel, and WolframAlpha.

Why Five Algorithms?

Different tools calculate quartiles differently. The same dataset can produce different Q1 and Q3 values depending on the method:

| Algorithm | Compatible With | Method | |-----------|----------------|--------| | Tukey's Hinges | Statistics textbooks, manual calculation | Median splitting (exact values) | | R-7 / Python | R quantile(type=7), NumPy, SciPy, Google Sheets | Linear interpolation h=(n-1)p+1 | | Excel INC | Excel QUARTILE.INC, LibreOffice, WPS | Hyndman-Fan Type 7 | | Excel EXC | Excel QUARTILE.EXC | Hyndman-Fan Type 6 h=(n+1)p | | WolframAlpha | WolframAlpha, Mathematica, R type=5 | R-5 interpolation h=np+0.5 |

🔗 See it in action: Interactive Algorithm Comparison on PlotNerd.com

Install

npm install @plotnerd/stat-engine

Also works with yarn, pnpm, and bun:

yarn add @plotnerd/stat-engine
pnpm add @plotnerd/stat-engine
bun add @plotnerd/stat-engine

Quick Start

import { MultiAlgorithmEngine } from '@plotnerd/stat-engine';

// Calculate with all 5 algorithms at once
const data = [6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49];
const results = MultiAlgorithmEngine.calculateAllAlgorithms(data);

// Access any algorithm's results
console.log(results.r_python_default.q1);     // 25.5
console.log(results.r_python_default.q3);     // 42.5
console.log(results.r_python_default.iqr);    // 17

// Full five-number summary
console.log(results.tukey_hinges.fiveNumberSummary);
// [6, 25.5, 40, 42.5, 49]

Each algorithm result includes:

{
  minimum, maximum, count, sum, mean,   // Basic stats
  q1, median, q3, iqr,                  // Quartiles
  fiveNumberSummary,                     // [min, Q1, median, Q3, max]
  outliers, outlierIndices,              // Outlier detection
  lowerFence, upperFence,               // 1.5×IQR fences
  dataRange, calculationTime             // Metadata
}

API

MultiAlgorithmEngine.calculateAllAlgorithms(data)

Calculate results using all five algorithms. Returns outliers, fences, IQR, mean, and five-number summary for each.

const results = MultiAlgorithmEngine.calculateAllAlgorithms([1, 2, 3, 4, 5, 6, 7, 8]);
// results.tukey_hinges, results.r_python_default, results.excel_inclusive, etc.

MultiAlgorithmEngine.calculateQuartiles(sortedData, algorithm)

Calculate quartiles using a specific algorithm.

const sorted = [1, 2, 3, 4, 5, 6, 7, 8];
const { q1, median, q3 } = MultiAlgorithmEngine.calculateQuartiles(sorted, 'r_python_default');

Available algorithms: tukey_hinges | r_python_default | excel_inclusive | excel_exclusive | wolfram_alpha

MultiAlgorithmEngine.compareAlgorithms(results, baseAlgorithm?)

Compare all algorithms against a baseline (default: r_python_default). Returns differences classified as identical, minor, significant, or major.

const results = MultiAlgorithmEngine.calculateAllAlgorithms(data);
const comparisons = MultiAlgorithmEngine.compareAlgorithms(results);
comparisons.forEach(c => console.log(`${c.algorithm}: ${c.significance}`));

MultiAlgorithmEngine.recommendAlgorithm(data, context?)

Get a smart recommendation based on data characteristics and user context.

const rec = MultiAlgorithmEngine.recommendAlgorithm(data, {
  userSoftware: 'Excel',   // → recommends excel_inclusive
  useCase: 'teaching',      // → recommends tukey_hinges
  experience: 'beginner'    // → recommends tukey_hinges
});
console.log(rec.recommended, rec.confidence); // 'excel_inclusive', 0.95

MultiAlgorithmEngine.generateVerification(options)

Generate verification code and links for R, Python, Excel, or WolframAlpha.

const verify = MultiAlgorithmEngine.generateVerification({
  algorithm: 'wolfram_alpha',
  data: [1, 2, 3, 4, 5]
});
console.log(verify.verificationUrl);  // WolframAlpha link
console.log(verify.verificationCode); // Copy-paste code

MultiAlgorithmEngine.getAvailableAlgorithms()

Returns metadata for all five algorithms, including name, description, category, compatible software, and precision type.

MultiAlgorithmEngine.getAlgorithmMetadata(algorithm)

Returns metadata for a specific algorithm.

Utility Functions

import { calculateMedian, kahanSum, roundToPrecision } from '@plotnerd/stat-engine';

calculateMedian([1, 2, 3, 4, 5]);     // 3
kahanSum([0.1, 0.2, 0.3]);            // 0.6 (compensated)
roundToPrecision(3.14159, 2);          // 3.14

TypeScript Support

Full TypeScript support with exported types:

import type {
  QuartileAlgorithm,
  StatisticalResults,
  MultiAlgorithmResults,
  AlgorithmComparison,
  AlgorithmRecommendation,
  VerificationResult,
} from '@plotnerd/stat-engine';

Numerical Accuracy

• Kahan summation for compensated floating-point addition
• Numerically stable median using overflow-safe midpoint calculation
• 4-decimal precision with epsilon-aware rounding
• 26 test cases covering edge cases, negative numbers, duplicates, and precision

Browser & Node.js Support

Works in both environments:

| Environment | Version | |-------------|---------| | Node.js | 16+ | | Chrome | 80+ | | Firefox | 80+ | | Safari | 14+ | | Edge | 80+ |

Used By

• PlotNerd.com — Professional quartile calculator & box plot creator with 10+ language support

Algorithm Details

For a deep dive into how each algorithm works and when to use which, check out:

• 📊 Quartile Methods Compared — Side-by-side analysis
• 📖 Tukey vs R-7: Which Method Should You Use? — In-depth comparison
• 🧮 Interactive Quartile Guide — Try it yourself
• 🎯 Why PlotNerd Is More Accurate — Accuracy deep dive

Contributing

Contributions are welcome! Please feel free to submit issues and pull requests.

git clone https://github.com/paradoxie/stat-engine.git
cd stat-engine
npm install
npm test

License

MIT © PlotNerd Team