A marine biologist is researching the relationship between the depth of a coral reef, ddd meters, and the number of distinct species, sss, identified at that depth. For a sample of n=12n = 12n=12 sites, the data is transformed using the coded variables u=d−1005u = \frac{d - 100}{5}u=5d−100 and v=s−204v = \frac{s - 20}{4}v=4s−20. The following summary statistics are recorded:
∑u=72Suu=150∑v=120Svv=600∑uv=505 \sum u = 72 \quad S_{uu} = 150 \quad \sum v = 120 \quad S_{vv} = 600 \quad \sum uv = 505 ∑u=72Suu=150∑v=120Svv=600∑uv=505Calculate the product-moment correlation coefficient for the coded variables uuu and vvv. Give your answer to 3 decimal places.
State the value of the product-moment correlation coefficient for the original variables ddd and sss.
The biologist suggests that deeper reef sites are likely to host a higher number of distinct species. Determine, with a reason, whether this suggestion is supported by the data.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.