Index of Dispersion Calculator
Measure the variability in your dataset relative to the mean with this statistical dispersion analyzer
Data Input
Calculation Options
Dispersion Analysis Results
Enter your data to analyze its dispersion characteristics.
Detailed Analysis
Your detailed dispersion analysis will appear here.
Data Visualization
📊 Statistical Reference Guide
| Measure | Formula | Interpretation | Ideal For |
|---|---|---|---|
| Index of Dispersion | σ²/μ | <1: Underdispersed, =1: Poisson, >1: Overdispersed | Count data, event occurrences |
| Coefficient of Variation | (σ/μ)×100% | Relative variability (lower = more consistent) | Comparing variability across different scales |
| Interquartile Range | Q3 - Q1 | Range of middle 50% of data | Robust measure for skewed distributions |
| Range | Max - Min | Total spread of data | Quick variability assessment |
Note: Interpretation depends on data type and context. Poisson distributions expect dispersion ≈1.
📚 Practical Applications
Biological Sciences
Analyze spatial distribution of organisms (clustered, random, or uniform).
Quality Control
Monitor manufacturing defects or process variability over time.
Call Centers
Assess consistency of call arrival patterns for staffing.
Actuarial Science
Evaluate claim frequency patterns in insurance data.
Epidemiology
Study disease occurrence patterns (clustered vs random).
Retail Analytics
Analyze customer arrival patterns for staffing needs.
Note: The Index of Dispersion is most meaningful for count data. For continuous data, consider using the coefficient of variation instead. Results should be interpreted in context with other statistical measures.