📐 Different Philosophical Approaches

Quartile calculation methods reflect two fundamental approaches to statistics:

• Resistant Methods (Tukey's Hinges): Prioritize robustness and interpretability. They split data at the median, making quartiles easy to understand and teach. This method is ideal for exploratory data analysis and educational contexts.
• Interpolation Methods (R-7, Excel, WolframAlpha): Use mathematical formulas to calculate positions, then interpolate between data points. These methods provide smooth, consistent results that work well in computational workflows and data science pipelines.

🔢 Historical Evolution

Each method emerged to solve specific problems:

• Tukey's Hinges (1977): Developed by John Tukey for exploratory data analysis. Designed to be intuitive and resistant to outliers.
• R-7 Method: Became the default in R and Python because it provides consistent, mathematically elegant results that work well with large datasets.
• Excel QUARTILE.INC: Uses R-6 method (similar to R-7) to ensure compatibility with spreadsheet workflows.
• WolframAlpha (R-5): Uses a slightly different interpolation formula, resulting in different quartile values for some datasets.

⚖️ No Universal Standard

The statistical community has never established a single "correct" quartile method. Each approach has valid use cases, and the choice often depends on your context, audience, and software ecosystem. The key is consistency—always document which method you're using and why.