The formula to calculate the Index of Qualitative Variation (IQV) is:
\[ IQV = \frac{K \left( 100^2 - \sum Pct^2 \right)}{100^2 \cdot (K-1)} \]
Where:
The Index of Qualitative Variation (IQV) is a statistical measure used to assess the diversity or variability within a qualitative data set. It quantifies the extent to which different categories or groups are represented in a dataset, indicating the diversity or heterogeneity of the examined variables.
IQV is calculated by dividing the sum of squared frequencies of each category or group by the square of the total number of observations. This results in a value ranging from 0 to 1, where 0 represents complete homogeneity (all observations belong to the same category) and 1 represents maximum heterogeneity (observations are evenly distributed across all categories).
Let's assume the following values:
Using the formula to calculate the IQV:
\[ \sum Pct^2 = 25^2 + 25^2 + 25^2 + 25^2 = 625 + 625 + 625 + 625 = 2500 \]
\[ IQV = \frac{4 \left( 100^2 - 2500 \right)}{100^2 \cdot (4-1)} = \frac{4 \left( 10000 - 2500 \right)}{10000 \cdot 3} = \frac{4 \cdot 7500}{30000} = \frac{30000}{30000} = 1 \]
The IQV is 1, indicating maximum heterogeneity.