Question 1: Plot the points (2, 5), (4, 7), (6, 9), and (8, 11) on the scatter graph. What trend do you observe?

Answer: The points show a positive linear trend, increasing together.

Question 2: Calculate the average (mean) of the x-values and y-values for the points plotted in Question 1.

Answer: {"mean_x":5,"mean_y":8}

Question 3: Given the data points (1, 2), (3, 4), (5, 6), (7, 8), plot these points and determine if there is a correlation. Is it positive, negative, or none?

Answer: Plotting these points shows a positive correlation, as y increases with x.

Question 4: Construct a scatter plot with the following data: hours studied (x) and test scores (y): (1, 50), (2, 55), (3, 65), (4, 70), (5, 80). Describe the relationship.

Answer: As hours studied increase, test scores tend to increase, showing a positive relationship.

Question 5: Calculate the line of best fit (approximate) for the points: (1, 2), (2, 3), (3, 5), (4, 4), (5, 6).

Answer: Approximate line: y = 0.9x + 1.2

Question 6: A scatter plot shows a clustering of points around y = 3x + 2. What does this suggest about the relationship between the variables?

Answer: There is a strong positive linear relationship between the variables.

Question 7: Identify and correct the mistake in the following statement: 'A scatter graph with points dispersed randomly indicates a strong correlation.'

Answer: Random dispersion indicates no correlation, not strong.

Question 8: Using the data set: (2, 10), (4, 20), (6, 30), (8, 40), plot the points and determine the strength of the correlation.

Answer: Points lie on a straight line, indicating a very strong positive correlation.

Question 9: For the data points: (1, 3), (2, 5), (3, 7), (4, 9), what is the approximate equation of the trend line?

Answer: y = 2x + 1

Question 10: Challenge: Given the data points (1, 2), (2, 4), (3, 8), (4, 16), plot these points. Describe the pattern and determine the mathematical relationship.

Answer: The points follow an exponential pattern, roughly y = 2^x.

Question 11: Identify a common mistake students might make when plotting bivariate data and explain how to avoid it.

Answer: Mistake: plotting x and y in the wrong order; avoid by labeling axes clearly and plotting according to (x, y).