📊 Index of Qualitative Variation Calculator
Enter the counts for each category (leave unused categories at 0) to compute the Index of Qualitative Variation, a measure of diversity for categorical data.
What this calculator does
The Index of Qualitative Variation (IQV) measures how spread out, or diverse, a set of categorical (non-numeric) observations is — for example, how evenly survey respondents are distributed across answer choices. It ranges from 0 (everyone in one category, no variation) to 1 (observations spread perfectly evenly across all categories, maximum variation).
How the calculation works
The calculator first converts each category’s count into a proportion of the total observations, then sums the squares of those proportions. The IQV formula is IQV = k / (k – 1) x (1 – sum of p_i squared), where k is the number of categories used and p_i is the proportion in category i. The k / (k-1) factor rescales the result so the maximum possible value is exactly 1, regardless of how many categories there are.
Leave any category you are not using set to 0 — it will be excluded from the category count automatically. This tool is intended for general statistics and survey-analysis education.