# Simpson’s Diversity Index Quiz

URL: https://speedycalculator.com/calculators/statistics/simpsons-diversity-index-quiz/
Last updated: 2026-10-30

> The Simpson's diversity index quiz is a practice tool that generates new questions on demand – calculating D, 1 − D or 1/D for random communities, comparing two habitats, or multiple-choice questions on interpretation – and checks your answer with a full worked solution.

## Inputs

- Question type
- Difficulty
- Your answer
- Solution

## Results

- Question
- Data
- Feedback
- Worked solution
- Your score

## Formula

```
D = Σn(n − 1) ÷ (N(N − 1)) · Simpson's diversity index = 1 − D · reciprocal index = 1/D
```

## Explanation

Reading a formula is one thing; using it under exam conditions is another. This practice page keeps throwing fresh Simpson's index problems at you so you can build speed and confidence. Each calculation question gives the number of individuals of several species and asks for D, 1 − D or 1/D to two decimal places. Comparison questions show two communities and ask which is more diverse, and concept questions test whether you can interpret the numbers – what a high D means, why ecologists use 1 − D and how the index relates to evenness.

Pick a question type and difficulty, type your answer and the page tells you at once whether it is right. The solution shows every step: the total N, the n(n − 1) column, the division and the final rounding. A running score counts how many you have answered correctly in this session, and "New question" draws another problem with different numbers.

Nothing is stored or sent anywhere – the questions are generated in your browser and the score resets when you reload the page.

### How to use the Simpson's Diversity Index Quiz

- **Question type**
- **Difficulty**
- **Your answer**
- **Solution**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Choose the question type (or "Mixed") and difficulty, read the question, type your answer – a number rounded to 2 decimal places, A/B for comparisons, or A–D for concept questions – and check the feedback. Numeric answers within ±0.005 of the exact value count as correct.

### Worked example

Question: a survey found 10, 6 and 4 individuals of three species – find D, 1 − D and 1/D. N = 20 and Σn(n − 1) = 90 + 30 + 12 = 132, so D = 132 ÷ (20 × 19) = 132 ÷ 380 = 0.3474 → 0.35. The diversity index is 1 − 0.3474 = 0.65 and the reciprocal index 1 ÷ 0.3474 = 2.88.

### Exam checklist

- Use N − 1, not N, in the denominator for counted samples.
- Do not forget the n − 1 for every species – a species with 1 individual contributes 0.
- Say which version you report: D, 1 − D or 1/D.
- Higher 1 − D or 1/D = more diverse; higher D = less diverse.

## Worked example

Inputs — Question type: Mixed – any type; Difficulty: Easy – 3 species, small counts; Your answer: ; Solution: Show after I answer.

Results — **Question = A sample has 1 − D close to 0. What is most likely true? Type the letter A, B, C or D.**; Data = A) There are many rare species
B) One species makes up almost all individuals
C) All species are equally common
D) The sample is very large; Feedback = Type your answer in the box above.; Your score = No questions answered yet.

## Key terms

- **Simpson's index D**: The probability that two individuals drawn without replacement belong to the same species.
- **Gini–Simpson index**: 1 − D, the probability that they belong to different species.
- **Inverse Simpson index**: 1/D, the effective number of equally common species.

## FAQ

**How do I calculate Simpson's index quickly?**
Write n(n − 1) next to every count, add that column, and divide by N(N − 1). For 10, 6 and 4: (90 + 30 + 12) ÷ (20 × 19) = 132 ÷ 380 = 0.35.

**How should I round my answer?**
To two decimal places. Answers within ±0.005 of the exact value are marked correct, so 0.35 is accepted for D = 0.3474.

**What is the quickest way to compare two communities?**
With the same number of species, the more even community is more diverse. Otherwise compute 1 − D for both – the higher value wins.

**Why does a higher D mean lower diversity?**
D is the chance that two random individuals are the same species; the more one species dominates, the higher that chance.

**Are the questions random?**
Yes. Counts and question types are drawn at random in your browser each time you press "New question".

**Is my score saved?**
No – it only counts the questions answered since the page was loaded, and nothing leaves your device.


## Sources

- [Wikipedia – Diversity index (Simpson index)](https://en.wikipedia.org/wiki/Diversity_index)
- [Simpson (1949), Measurement of diversity, Nature 163: 688](https://doi.org/10.1038/163688a0)