A random sample of 50 salmon was caught by a scientist - Edexcel - A-Level Maths Statistics - Question 1 - 2011 - Paper 1

The product moment correlation coefficient (r) is calculated using: $r = \frac{n \sum lw - \sum l \sum w}{\sqrt{(n \sum l^{2} - (\sum l)^{2})(n \sum w^{2} - (\sum w)^{2})}}$ Where (n = 50):

1. Calculating the numerator: $\text{Numerator} = 50 \times 29330.5 - 4027 \times 357.1$ $= 1466525 - 1437067.7 = 2947.3$
2. Calculating the denominator: $\text{Denominator} = \sqrt{(50 \times 327754.5 - (4027)^{2})(50 \times 289.6 - (357.1)^{2})}$ $= \sqrt{(16387725 - 16216029)(14480 - 127056.41)}$ $= \sqrt{171696 \times 1781.59}$ Calculate: $\approx 550668.8764 \approx 740.36$
3. Substituting back: $r = \frac{2947.3}{740.36} \approx 0.398 \approx 0.57 \text{ to 3 significant figures}$

The calculated correlation coefficient of approximately 0.57 indicates a moderate positive correlation between the length and weight of the salmon. This suggests that, generally, as the length of the salmon increases, their weight also tends to increase.