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

0.0000
Index of Qualitative Variation
No Variation
All observations belong to the same category

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)

0 (No Variation)0.5 (Moderate)1 (Maximum Variation)

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

0.00 - No Variation
All in one category
0.01-0.30 - Low
Concentrated distribution
0.31-0.70 - Moderate
Some spread across categories
0.71-0.90 - High
Good distribution
0.91-1.00 - Maximum
Nearly equal distribution

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.