Index of Qualitative Variation Calculator

Enter categories with counts to quantify diversity of nominal data on a 0–1 scale.

IQV

0.9933

High diversity (responses are well distributed).

Category distribution (total responses: 100)
CategoryCountProportion
Red3030.00%
Blue2020.00%
Green2525.00%
Yellow2525.00%

How to Use This Calculator

  1. List each category and its count, one per line.
  2. Ensure at least two categories have non-zero responses.
  3. Review the IQV and category proportions displayed.
  4. Use IQV to compare diversity across surveys or datasets.

Formula

IQV = (k / (k − 1)) × (1 − Σpi²)

k = number of categories, pi = proportion for category i

IQV ranges from 0 (no diversity) to 1 (maximum diversity). It equates to 1 − normalized Herfindahl index.

Full Description

The Index of Qualitative Variation summarizes categorical diversity, useful in sociology, marketing, and political science to compare how evenly responses are distributed. Unlike entropy, IQV maps to a 0–1 range, simplifying interpretation.

High IQV indicates responses are evenly spread across categories, while low IQV signifies concentration in a few categories.

Frequently Asked Questions

Can I include categories with zero counts?

Yes, but IQV considers the number of categories with any entry. Zero counts do not affect diversity unless all counts are zero.

How does IQV compare to entropy?

Both measure diversity, but IQV is scaled to 0–1 and emphasizes categorical uniformity, whereas entropy uses logarithms.

What happens if all responses fall into one category?

IQV equals zero, indicating no diversity.

Can IQV exceed 1?

No. By definition the index is capped at 1 when proportions are perfectly uniform.