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Testing proportional relationships in data
Sewage was accidentally added to a river. The sewage moved with the river water and affected the number of bacteria in the water and the concentration of dissolved oxygen in the water. Samples of river water were analysed at different distances from where the sewage was added. Table 2 shows the results.
| Distance from where sewage was added in km | Number of bacteria × 1000/mm³ | Concentration of dissolved oxygen in mg/dm³ |
|---|---|---|
| 0.0 | 4 | 5.4 |
| 1.0 | 75 | 4.8 |
| 2.0 | 125 | 4.3 |
| 3.0 | 145 | 3.8 |
| 4.0 | 160 | 3.3 |
| 5.0 | 216 | 2.7 |
Explain why the student’s conclusion is not correct. Use Table 2.
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Marking points
- 1 Identifies from Table 2 that bacteria increase while dissolved oxygen decreases, or states that the correlation is negative.
- 2 Explains why this is not direct proportionality: the quantities do not increase together in a constant ratio.
Full-mark answer
Table 2 shows a negative correlation: as bacteria increase from 4 to 216 × 1000/mm³, dissolved oxygen decreases from 5.4 to 2.7 mg/dm³. Direct proportionality would mean that both quantities increase together in the same ratio, so the student’s conclusion is not correct.
Why this answer loses marks
They are inversely proportional.
That label is ignored on its own; state the negative trend in the table and explain what direct proportionality would require.