Enter the proportion of each category in the population into the calculator to determine the Blau Index of diversity.

## Blau Index Formula

The following formula is used to calculate the Blau Index of diversity.

BI = 1 - ∑ (p_i)^2

Variables:

• BI is the Blau Index of diversity
• p_i is the proportion of each category in the population

To calculate the Blau Index, square the proportion of each category in the population. Sum up these squared proportions. Subtract the sum from 1. The result is the Blau Index, which ranges from 0 (no diversity) to 1 (maximum diversity).

## What is a Blau Index?

The Blau Index, also known as the Index of Heterogeneity, is a statistical measurement used to quantify the level of diversity within a group. Developed by sociologist Peter Blau, the index ranges from 0 to 1, where 0 indicates no diversity (everyone in the group is from the same category) and 1 indicates maximum diversity (each individual in the group is from a different category). The Blau Index is commonly used in social sciences to measure diversity in areas such as race, ethnicity, or gender within a population.

## How to Calculate Blau Index?

The following steps outline how to calculate the Blau Index:

1. First, determine the proportion of each category in the population (p_i).
2. Next, square each proportion (p_i^2).
3. Next, sum up all the squared proportions (∑ (p_i^2)).
4. Finally, subtract the sum from 1 (BI = 1 - ∑ (p_i^2)).
5. After inserting the proportions and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Proportion of Category A (p_a) = 0.4

Proportion of Category B (p_b) = 0.3

Proportion of Category C (p_c) = 0.2

Proportion of Category D (p_d) = 0.1