A marine biology team monitored the biodiversity of benthic macroinvertebrate communities in a coastal estuary over 10 consecutive quarters following an environmental restoration program. The index of diversity (ddd) for each quarter was calculated and recorded in the table below.
| Quarter | Index of diversity (ddd) |
|---|---|
| Quarter 1 | 1.8 |
| Quarter 2 | 3.5 |
| Quarter 3 | 4.2 |
| Quarter 4 | 3.5 |
| Quarter 5 | 5.1 |
| Quarter 6 | 2.9 |
| Quarter 7 | 3.5 |
| Quarter 8 | 6.3 |
| Quarter 9 | 3.5 |
| Quarter 10 | 4.0 |
The team used the standard formula to calculate the index of diversity (ddd):
d=N(N−1)∑n(n−1) d = \frac{N(N-1)}{\sum n(n-1)} d=∑n(n−1)N(N−1)where:
In certain quarters, the recorded raw data yielded N=210N = 210N=210 and ∑n(n−1)=12540\sum n(n-1) = 12540∑n(n−1)=12540. Determine which quarters corresponded to these values. Show your calculations clearly.
