Credit Sprint / Practice problems / Simpson's diversity index

Simpson's diversity index practice problems

Biology Unit 8. Try each one, then open the worked solution. The Credit Sprint app generates unlimited new versions with fresh numbers.

Problem 1.

A sample has 9 oaks, 3 maples and 4 pines. Using D = 1 − Σ(n/N)², what is Simpson's diversity index? (Round to 2 decimals.)

Show solution

N = 16. Σ(n/N)² = (9/16)² + (3/16)² + (4/16)² = 0.414. D = 1 − 0.414 = 0.59.

Problem 2.

A sample has 8 oaks, 6 maples and 5 pines. Using D = 1 − Σ(n/N)², what is Simpson's diversity index? (Round to 2 decimals.)

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N = 19. Σ(n/N)² = (8/19)² + (6/19)² + (5/19)² = 0.346. D = 1 − 0.346 = 0.65.

Problem 3.

A sample has 7 oaks, 6 maples and 1 pines. Using D = 1 − Σ(n/N)², what is Simpson's diversity index? (Round to 2 decimals.)

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N = 14. Σ(n/N)² = (7/14)² + (6/14)² + (1/14)² = 0.439. D = 1 − 0.439 = 0.56.

Problem 4.

A sample has 2 oaks, 3 maples and 5 pines. Using D = 1 − Σ(n/N)², what is Simpson's diversity index? (Round to 2 decimals.)

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N = 10. Σ(n/N)² = (2/10)² + (3/10)² + (5/10)² = 0.38. D = 1 − 0.38 = 0.62.

Problem 5.

A sample has 2 oaks, 9 maples and 6 pines. Using D = 1 − Σ(n/N)², what is Simpson's diversity index? (Round to 2 decimals.)

Show solution

N = 17. Σ(n/N)² = (2/17)² + (9/17)² + (6/17)² = 0.419. D = 1 − 0.419 = 0.58.

Problem 6.

A sample has 7 oaks, 3 maples and 4 pines. Using D = 1 − Σ(n/N)², what is Simpson's diversity index? (Round to 2 decimals.)

Show solution

N = 14. Σ(n/N)² = (7/14)² + (3/14)² + (4/14)² = 0.378. D = 1 − 0.378 = 0.62.