Question 1: Calculate the correlation coefficient (r) approximately for the given data points: (2, 5), (4, 9), (6, 11), (8, 15).

Answer: 0.99

Question 2: Plot the points (1, 2), (3, 4), (5, 6), (7, 8) on the grid and describe the type of correlation.

Answer: Positive correlation

Question 3: Construct a scatter plot for the data: hours studied vs. test scores: (1, 50), (2, 55), (3, 65), (4, 70), (5, 80). What does the graph indicate about the correlation?

Answer: Strong positive correlation

Question 4: Identify the main difference between no correlation, positive correlation, and negative correlation in a scatter graph.

Answer: No correlation shows no relationship; positive correlation shows variables increase together; negative shows one increases while the other decreases.

Question 5: A scatter plot shows a perfect downward line. What is the correlation coefficient, and what does this indicate?

Answer: -1 or -1.0, indicating a perfect negative correlation

Question 6: In a data set, some points are outliers that don't fit the overall trend. How can these affect the correlation coefficient?

Answer: Outliers can weaken or distort the apparent correlation, making it seem weaker or stronger than it actually is.

Question 7: Given the data points: (1, 3), (2, 5), (3, 7), (4, 9), (5, 11), draw and interpret the scatter graph.

Answer: The points form a straight line with positive slope, indicating a strong positive correlation.

Question 8: Suppose you observe a scatter plot with no clear pattern. What are possible reasons for this, and how might it influence your analysis?

Answer: Possible reasons include random data, outliers, or a true lack of relationship. It suggests no correlation.

Question 9: Identify and correct the mistake in this statement: 'A perfect positive correlation means the data points form a completely random scatter on the graph.'

Answer: Incorrect; a perfect positive correlation means the data points form a straight line with positive slope.

Question 10: A student draws a scatter plot showing a weak negative correlation but claims it is positive. How should you explain the mistake?

Answer: The points tend to decrease together, indicating negative correlation; the student misinterpreted the trend.

Question 11: Given the data: (1, 10), (2, 15), (3, 20), (4, 25), (5, 30). Predict the next data point assuming the trend continues, and plot it.

Answer: Next point: (6, 35); students should plot and confirm the linear trend continues.