What Is Dispersion?
Dispersion (or spread) describes how spread out the values in a dataset are. While central tendency tells you the typical value, dispersion tells you how much individual values deviate from that typical value. High dispersion means data is widely scattered; low dispersion means values cluster tightly around the center.
Understanding dispersion is critical for risk assessment, quality control, investment analysis, and scientific measurement. Two datasets can have identical means but vastly different dispersions, leading to very different practical implications.
Measures of Dispersion
| Measure | Formula | Robust? |
|---|---|---|
| Range | Max - Min | No |
| IQR | Q3 - Q1 | Yes |
| Variance | Σ(xi-x̄)²/(n-1) | No |
| Std Dev | √Variance | No |
| CV | (SD/Mean)×100 | No |
| MAD | Median(|xi-median|) | Yes |
Formulas
Comparing Measures
Range is simplest but most sensitive to outliers. IQR ignores extremes by focusing on the middle 50%. Standard deviation is the most common measure but is affected by outliers. CV enables comparison between datasets with different units or scales.
Frequently Asked Questions
When should I use IQR instead of standard deviation?
Use IQR when data has outliers or is heavily skewed. IQR only considers the middle 50%, making it robust to extreme values that inflate standard deviation.
What is a good coefficient of variation?
CV below 15% is often considered low variability, 15-30% moderate, and above 30% high. But acceptable CV depends entirely on the field and application.
Can dispersion be negative?
No. All measures of dispersion are non-negative. They equal zero only when all values in the dataset are identical (no spread at all).