Why Excel, R, Python, SPSS
Calculate Different Quartiles?
Deep analysis of mainstream statistical software quartile algorithm differences, providing complete compatibility solutions and best practice guidance.
π€ Problem Discovery: Same Data, Different Results
Real Case
A data analyst was processing a dataset with 11 values [6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49] when they discovered Excel calculated Q1=15.0, while R language yielded Q1=25.5, Python also returned 25.5, but SPSS gave yet another different result...
This isn't a software bug, but algorithm standard differences!
In data science and statistical analysis work, cross-platform result consistency is an often overlooked but extremely important issue. When we use different statistical software to calculate quartiles, we often encounter subtle but significant differences.
Why does this happen?
- Historical reasons: Different software developed in different eras adopted the "best practices" of their time
- Lack of standardization: The statistical community has no absolute unified standard for quartile calculation methods
- User requirements: Different fields and user groups have different precision and compatibility requirements
- Backward compatibility: Software vendors need to maintain compatibility with historical versions
π¬ In-Depth Algorithm Analysis: 4 Mainstream Methods
π Method 1: Tukey Hinges (Textbook Method)
Algorithm Principle
Based on median splitting method, recursively divides data into two halves. Q1 is the median of the lower half, Q3 is the median of the upper half.
Advantages
- β’ Results are always values from original data
- β’ Easy for manual calculation and understanding
- β’ Statistics textbook standard
Calculation Steps
1. Sort data
2. Find median position
3. Split into lower and upper halves
4. Calculate median of each half
Result: Q1=data value, Q3=data value
π Method 2: R-7/Python Standard (Linear Interpolation)
Algorithm Principle
Uses formula h = (n-1)*p + 1 to determine quantile position, then performs linear interpolation between adjacent data points.
Advantages
- β’ Modern statistical software standard
- β’ Excellent mathematical properties
- β’ Widely adopted in research papers
Calculation Formula
h = (n-1) * p + 1
Q1: p=0.25, h=(n-1)*0.25+1
Q3: p=0.75, h=(n-1)*0.75+1
If h is not integer, perform linear interpolation
π₯οΈ Software Comparison: Excel vs R vs Python vs SPSS
| Software | Default Method | Function/Command | Main User Groups |
|---|---|---|---|
| π»
Microsoft Excel
Business analysis standard
| QUARTILE.INC | =QUARTILE.INC(A1:A10,1) |
Business analysts Finance professionals |
| π R Language
Statistical computing standard
| type=7 | quantile(data, c(0.25,0.75)) |
Statisticians Data scientists |
π Practical Examples: Specific Difference Demonstration
Test Dataset
[6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49] Data size: n=11, Source: Statistics textbook standard case
π Textbook Method
π R/Python
π» Excel
π‘ Best Practices: How to Choose and Unify Standards
π Academic Research Scenario
Recommended Method
R-7/Python Standard (Linear Interpolation)
Reasons
- β’ Widely accepted in journal papers
- β’ Good reproducibility
- β’ High cross-software consistency
πΌ Business Analysis Scenario
Recommended Method
Excel QUARTILE.INC
Reasons
- β’ Compatible with Office suite
- β’ Familiar to non-technical users
- β’ Standardized report format
π Teaching Scenario
Recommended Method
Tukey Hinges (Textbook Method)
Reasons
- β’ Easy for manual calculation verification
- β’ Results are actual data values
- β’ Concept-friendly understanding
π― Summary & Recommendations
Key Points Summary
Problem Essence
- β Quartile algorithms historically have multiple standards
- β Different software uses different default methods
- β Same data may produce significantly different results
- β This is an algorithm standard issue, not software error
Solutions
- β Choose appropriate algorithm based on use case
- β Unify calculation standards within teams
- β Use multi-algorithm comparison tools to verify results
- β Clearly specify the method used in reports
Solve Quartile Compatibility Issues Now
Use PlotNerd's multi-algorithm comparison feature to verify calculation results from different software with one click, and choose the algorithm standard that best fits your needs.
π¬ Interactive Comparison Tool
Want to see exactly how different methods calculate quartiles with your own data? Use our Interactive Guide to Quartile Calculation Discrepancies to compare Tukey's Hinges, R-7, Excel QUARTILE.INC, and WolframAlpha methods side-by-side with step-by-step calculations and visual comparisons.
Open Interactive Guideπ Related Articles
- β Interactive Guide to Quartile Calculation Discrepancies β Compare methods side-by-side with your data
- β Box Plot in Excel (2025) β Step-by-Step Guide
- β Why Are There So Many Quartile Methods? A Deep Dive into Tukey's Hinges
- β Tukey's Hinges vs. R-7 Quantiles: How to Pick the Right Quartile Method
- β How to Compare Multiple Groups with Grouped Box Plots
- β MAD vs Tukey: Choosing the Right Outlier Detection Method
- β Understanding Notched Box Plots: Statistical Significance Visualization