IQR Calculator

Interquartile Range Calculator: Complete Guide

What Is It?

The Interquartile Range (IQR) Calculator is a statistical tool that measures data dispersion by analyzing the middle 50% of values. It calculates:

• Quartiles (Q1, Q3)
• Median
• IQR (Q3-Q1)
• Outlier boundaries
• Visual data distribution

Key Formulas

1. Q1 Calculation:
   Position = (n+1)/4
   Value = Linear interpolation if position isn’t integer

2. Q3 Calculation:
   Position = 3(n+1)/4
   Value = Linear interpolation if position isn’t integer

3. IQR Formula:

   $$IQR = Q3 - Q1$$

4. Outlier Boundaries:
   Lower Bound = Q1 - 1.5×IQR
   Upper Bound = Q3 + 1.5×IQR

How to Use

1. Input Data: Enter comma-separated values (e.g., 5,12,7,18,22)
2. Automatic Calculation: Results update in real-time
3. Interpret Output:
   • Box plot visualization
   • Color-coded outlier indicators
   • Detailed quartile values
4. Advanced Features:
   • Sample datasets for quick testing
   • Calculation history tracking
   • Step-by-step methodology

FAQs

Q: Why use IQR instead of range?
A: IQR eliminates distortion from extreme values, providing more reliable dispersion measurement.

Q: How are quartiles calculated?
A: We use the exclusive median method (Type 7) matching most statistical software.

Q: What defines an outlier?
A: Values falling below Q1-1.5×IQR or above Q3+1.5×IQR.

Terminology

• Quartile: Values dividing data into four equal parts (Q1=25th percentile, Q3=75th percentile)
• Median: Middle value (50th percentile)
• Whiskers: Lines extending to min/max non-outlier values
• Data Dispersion: Spread of dataset values
• Five-Number Summary: Min, Q1, Median, Q3, Max

Best Practices

1. Clean data before analysis (remove NA values)
2. Compare IQR across similar datasets
3. Always visualize distributions alongside calculations
4. Consider data context when interpreting outliers