Index of Qualitative Variation Calculator
Measure variability for categorical data with the IQV statistical index
Calculate Index of Qualitative Variation
Number of distinct categories in your data
Category Frequencies
IQV Results
Calculation Details
Formula: IQV = K(10,000 - ∑p²) / [10,000(K - 1)]
Number of categories (K): 2
Sum of squared percentages (∑p²): 0.00
Numerator: 2 × (10,000 - 0.00) = 20000.00
Denominator: 10,000 × (2 - 1) = 10000.00
IQV Scale (0 to 1)
Example: Ice Cream Flavor Preferences
Survey Data
Vanilla: 25 customers (25%)
Chocolate: 25 customers (25%)
Strawberry: 25 customers (25%)
Mint: 25 customers (25%)
Total: 100 customers, K = 4 categories
Calculation
∑p² = 25² + 25² + 25² + 25² = 625 + 625 + 625 + 625 = 2,500
IQV = 4(10,000 - 2,500) / [10,000(4 - 1)]
IQV = 4(7,500) / [10,000 × 3] = 30,000 / 30,000
IQV = 1.0000 (Maximum Variation)
Perfect equal distribution - no clear favorite flavor
IQV Interpretation
Tips
IQV is specifically for nominal (categorical) data
Values range from 0 (no variation) to 1 (maximum variation)
Higher IQV means more diverse/heterogeneous data
Useful for comparing diversity across different groups
Understanding Index of Qualitative Variation (IQV)
What is IQV?
The Index of Qualitative Variation (IQV) is a statistical measure that quantifies the amount of variability in nominal (categorical) data. Unlike measures of central tendency, IQV focuses on how spread out or diverse your categorical data is across different categories.
When to Use IQV?
- •Analyzing survey responses with categorical options
- •Measuring diversity in demographics data
- •Comparing variation across different groups
- •Ecological diversity studies
IQV Formula
IQV = K(10,000 - ∑p²) / [10,000(K - 1)]
- IQV: Index of Qualitative Variation (0 to 1)
- K: Number of categories
- ∑p²: Sum of squared percentages
- 10,000: Constant (100² for percentage calculations)
Key Point: IQV reaches its maximum value of 1.0 when observations are distributed equally across all categories, indicating maximum diversity.