Question 1: Plot the following points on the grid: (2, 3), (4, 5), (6, 7). Connect the points with a straight line.

Answer: Correct plot with straight line connecting points

Question 2: Calculate the correlation coefficient between the data points (1, 2), (3, 4), (5, 6). (Approximate answer)

Answer: Close to +1 indicating strong positive correlation

Question 3: Given a scatter graph showing a positive trend, explain what this indicates about the relationship between the two variables.

Answer: As one variable increases, the other also tends to increase, indicating a positive correlation.

Question 4: Construct a scatter graph showing the following data: (2, 4), (4, 8), (6, 12).

Answer: Points correctly plotted with a clear positive linear trend

Question 5: Identify whether the data points (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) show a positive, negative, or no correlation.

Answer: Negative correlation

Question 6: A scatter graph shows data points with no clear pattern. What does this suggest about the relationship between the variables?

Answer: There is little or no correlation between the variables.

Question 7: If the data points form a perfect straight line, what is the correlation coefficient?

Answer: Exactly +1 or -1 depending on the trend

Question 8: A teacher collects data on students' study hours and test scores. The scatter graph shows a positive trend. Explain how this information can be used to improve student performance.

Answer: Encourage students to increase study hours, as more hours are associated with higher scores.

Question 9: Determine if the following set of points shows a strong, moderate, or weak correlation: (1, 2), (2, 4), (3, 6), (4, 8).

Answer: Strong positive correlation

Question 10: A scatter plot shows a downward trend. What does this indicate about the relationship between the two variables?

Answer: As one variable increases, the other decreases, indicating a negative correlation.

Question 11: Identify a common mistake students make when plotting points on a scatter graph and suggest how to correct it.

Answer: Incorrectly plotting x and y coordinates; students should verify each point’s (x, y) position before plotting.

Question 12: Challenge: Given the data points (2, 3), (4, 7), (6, 11), (8, 15), determine the type of correlation and justify your answer.

Answer: Strong positive correlation; as x increases, y increases proportionally, indicating a linear trend.