Question 1: Plot the points (2, 5), (4, 7), (6, 9) and (8, 11) on the grid. Describe the pattern you observe.

Answer: Points lie roughly on a straight line with positive correlation.

Question 2: Calculate the correlation coefficient (rough estimate) for the data points: (1, 2), (2, 4), (3, 6), (4, 8).

Answer: Close to +1, indicating strong positive correlation.

Question 3: A dataset shows that as the number of hours studied increases, exam scores tend to increase. What type of correlation is this?

Answer: Positive correlation

Question 4: Construct a scatter graph plotting the following data: hours studied (x): 1, 2, 3, 4, 5; exam scores (y): 50, 55, 60, 65, 70.

Answer: Students should plot points that form a straight line with positive slope.

Question 5: Identify the outlier in the following data points: (1, 2), (2, 4), (3, 6), (4, 15). Explain your reasoning.

Answer: The point (4, 15) is an outlier as it does not fit the linear pattern of the other points.

Question 6: Estimate the line of best fit for the data: (1, 3), (2, 5), (3, 7), (4, 9).

Answer: Line approximately y = 2x + 1.

Question 7: In a health study, the number of hours exercised per week is plotted against weight loss. A strong positive correlation is observed. What does this imply?

Answer: More exercise is associated with greater weight loss.

Question 8: Plot the points: (1, 2), (2, 4), (3, 6), (4, 8). What pattern does this suggest?

Answer: The points lie on a straight line, indicating a perfect linear relationship with positive slope.

Question 9: A company records data on advertising spend (x) and sales revenue (y). The data points suggest a positive trend with some variability. How would you describe the relationship?

Answer: There is a positive correlation with some scatter, indicating that increased advertising generally increases sales.

Question 10: Identify a potential mistake when plotting data that shows no apparent correlation. How would you correct it?

Answer: Mistake: Incorrect plotting or axis scaling. Correction: Recheck data points and ensure axes are correctly scaled.

Question 11: Using the data points (1, 2), (2, 4), (3, 6), (4, 8), explain why the correlation coefficient is close to +1.

Answer: All points lie close to a straight line with positive slope, indicating a strong positive linear relationship.

Question 12: A scatter graph shows a clear downward trend. What is the nature of the correlation?

Answer: Negative correlation