1. **Problem Statement:** We have a scatter diagram showing scores of 10 students in Maths (x-axis) and English (y-axis) exams. (a) Identify the type of correlation shown by the graph. (b) Predict the English score for a pupil who scored 60 in Maths but missed the English exam, using the line of best fit. 2. **Understanding Correlation:** Correlation measures the relationship between two variables. It can be: - Positive correlation: as one variable increases, the other also increases. - Negative correlation: as one variable increases, the other decreases. - No correlation: no clear pattern. 3. **Analyzing the Graph:** The scatter plot shows points descending from near (10, 85) to (90, 25), indicating that as Maths scores increase, English scores decrease. 4. **Answer to (a):** This is a **negative correlation** because the line of best fit slopes downward. 5. **Using the Line of Best Fit for Prediction:** The line passes approximately through points (10, 85) and (90, 25). 6. **Find the equation of the line:** Slope $m = \frac{25 - 85}{90 - 10} = \frac{-60}{80} = -\frac{3}{4}$. Using point-slope form with point (10, 85): $$y - 85 = -\frac{3}{4}(x - 10)$$ Simplify: $$y = -\frac{3}{4}x + \frac{3}{4} \times 10 + 85 = -\frac{3}{4}x + 7.5 + 85 = -\frac{3}{4}x + 92.5$$ 7. **Predict English score for Maths = 60:** $$y = -\frac{3}{4} \times 60 + 92.5 = -45 + 92.5 = 47.5$$ 8. **Interpretation:** The predicted English score for the pupil who scored 60 in Maths is approximately **47.5**. **Final answers:** - (a) Negative correlation. - (b) Predicted English score is approximately 47.5.