Question 1: A student plotted a scatter graph showing the relationship between hours studied and test scores. The points seem to form a downward trend. What common misconception might the student have about correlation?

Answer: They might think a negative trend means more study causes lower scores, but correlation does not imply causation.

Question 2: A scatter graph shows data points with no clear pattern. What does this indicate about the correlation?

Answer: It indicates there is no correlation or a very weak correlation.

Question 3: Identify and correct the mistake: A student draws a scatter plot with points all aligned in a straight line but labels the axes incorrectly, leading to a wrong interpretation of the data.

Answer: The mistake is in the label of axes; correcting axis labels ensures correct interpretation.

Question 4: Plot the graph of y = 2x for x values 0 to 5 on the grid.

Answer: Students draw points at (0,0), (1,2), (2,4), (3,6), (4,8), (5,10).

Question 5: A scatter graph shows a perfect positive correlation. Identify a common mistake when drawing such a graph and how to avoid it.

Answer: Mistake: plotting points inaccurately. To avoid, check each point carefully and use a ruler if needed.

Question 6: Explain why a strong positive correlation does not mean one variable causes the other to increase.

Answer: Correlation shows a relationship, but does not prove causation. Other factors may influence both variables.

Question 7: A student incorrectly interprets a scattered diagram with a slight upward trend as having no correlation. What misconception are they making?

Answer: They think any trend means perfect correlation; but slight upward trends indicate weak positive correlation.

Question 8: Construct a scatter plot showing a weak negative correlation. Briefly describe how the points should be arranged.

Answer: Points should generally slope downward from left to right, but with some scatter and variability.

Question 9: Identify the common mistake in the following interpretation: 'Because two variables are correlated, one must cause the other.'

Answer: This is a misconception; correlation does not imply causation.

Question 10: A student notices a scatter graph with points spread randomly and concludes there is no relationship. Is this correct? Explain.

Answer: Yes, random spread indicates no correlation; they are correct in their conclusion.

Question 11: Error Analysis: A student plots data points on a scatter graph but forgets to include some points. How does this mistake affect the analysis?

Answer: Missing points can distort the perceived relationship, leading to incorrect conclusions about correlation.

Question 12: A scatter plot shows a clear linear pattern, but the student mislabels the axes, leading to a wrong interpretation of the data. What is the most important step to avoid this mistake?

Answer: Always verify and correctly label axes before analyzing the data.