# Index of Qualitative Variation Calculator

Created by Mariamy Chrdileli and Davide Borchia
Reviewed by Rijk de Wet
Last updated: Jan 18, 2024

Welcome to the Omni index of qualitative variation calculator, or IQV calculator — a simple and convenient tool to help you calculate variability for nominal variables.

Whether you're trying to explore the diversity of species in different ecological communities or the variability of sales across different product categories, you are at the right place. Use this index of qualitative variation calculator, and read on to get clear answers to some IQV-related questions, such as:

• What is the definition of the index of qualitative variation?
• What is the use of the IQV in statistics?
• How do I calculate the IQV?
• What is the formula of IQV?

And more!

🔎 Are you interested in descriptive statistics? You may also enjoy the dispersion calculator and descriptive statistics calculator while you're here.

## What is Index of qualitative variation (IQV) in statistics?

Let's start from the beginning — what is variation in statistics? The variation is the degree to which data points are dispersed from the central tendency of the data. The index of qualitative variation (IQV) measures variability for nominal variables (the type of categorical variables that represent data in categories without intrinsic order). To calculate the index, you need to know the following:

1. The number of categories in the variable; and
2. The sum of the squared percentages of each category.

For example, if you have two ice cream flavor categories and you have an equal amount of frequency observed for each ice cream, i.e., 50%, the sum of squared percentages would be 502 + 502 = 2,500 + 2,500 = 5,000.

The IQV can vary from 0 to 1, where 0 indicates no variability and 1 indicates maximum variability. Keep reading to find out how to calculate the IQV.

## How to calculate the index of qualitative variation

Now that you know the definition of the index of qualitative variation, you can take a look at $IQV$ formula below:

$\footnotesize \text{IQV} = \frac{\text{K}(100^2 - \Sigma\ p^2)}{100^2(\text{K} - 1)}$

where:

• $\text{IQV}$ — Index of qualitative variation;
• $K$ — The number of categories; and
• $\Sigma\ p^2$ — The sum of all squared percentages.

## An example of the IQV calculation

To better understand the concept, let's discuss an extreme example of IQV calculation, where we observe maximum variability.

Suppose you're running a café, and you want to see the most popular ice cream flavor out of the 4 options on your menu. At the end of the day, you discover that each ice cream flavor was sold with equal frequency, resulting in a distribution of 25% for each flavor. Here, you have the following data to calculate IQV:

• $K = 4$ (four ice-cream categories); and
• $\Sigma\ p^2 = 2,\!500$ (since the squared percentage for each ice cream is $25^2$ and we have 4 categories).

If you were to input the given data in the formula, you would get the following result:

\footnotesize \begin{align*} \text{IQV} &= \frac{\text{K}(100^2 - \sum p^2)}{100^2(\text{K} - 1)}\\[1.3em] &= \frac{4(10{,}000 - 2{,}500)}{10{,}000(4 - 1)}\\[1.3em] &= \frac{4\cdot7{,}500}{10{,}000\cdot3} \\[1.3em] &=1 \end{align*}

As mentioned before, when $\text{IQV} = 1$, we observe the maximum variability. This means there is no clear favorite ice cream flavor among your customers. Hence, you can use this index as an insight for your café.

## How to use our IQV calculator

You can use our index of qualitative variation calculator, whether you know only the sum of the squared percentages $\sum p^2$, or you know the precise values of each category separately. Choose the desired type of input at the top of the page!

If you choose to input the single categories manually, after you insert the desired number of categories $K$, we will show you the appropriate number of variables. The calculator will wait until the number of inputs matches the value of $K$. Once you fill in all the required categories, we will show you the values of $P$ and of the index of qualitative variation.

🙋 If you input the categories individually, you can also choose to visualize your inputs with a table and a pie chart: choose it at the bottom of the calculator!

## FAQ

### For what type of data do we use IQV?

The index of qualitative variation (IQV) can be used when dealing with nominal data. In other words, when you want to determine variability for data that can be divided into categories or groups. You can learn about the IQV formula by visiting the Omni index of qualitative variation calculator.

### How do I calculate the IQV?

To calculate the IQV:

1. Determine the number of categories and the sum of all squared percentages of observations.

2. Subtract the sum of all squared percentages from 10,000, and multiply it by the number of categories.

3. Subtract 1 from the number of categories, and multiply it by 10,000.

4. Divide the calculated number in Step 2 by the calculated number in Step 3 to obtain the IQV.

### Can the IQV be 0?

The IQV can be 0, indicating that all observations in your dataset belong to the same category or value. In other words, the data is homogenous and has no variability. On the other hand, if the IQV equals 1, the dataset has maximum variability.

### What does the IQV of 1 mean?

The IQV of 1 indicates the maximum variability and heterogeneity in the dataset. On the other hand, an IQV value of 0 indicates no variability in the data (i.e., all observations belong to the same category).

Mariamy Chrdileli and Davide Borchia
Input type
Sum of percentages
Number of categories
The sum of all squared percentages (∑p²)
The index of qualitative variation (IQV)
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