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MDM4U - Mathematics of Data Management 12 (2025-26) - A

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Question textEach student was shown a different scatter plot comparing two numerical variables. Each student described the variables being compared, estimated the correlation coefficient (r), described the strength and direction of the relationship, and explained the trend using the form “As ___ increases, ___ increases/decreases.”Match each student’s reasoning to the explanation that best fits their thinking. Student A:"I looked at a scatter plot comparing hours of sleep per night and reaction time on a reflex test. I said the correlation was r = -0.5, indicating a moderate negative linear relationship. As sleep increases, reaction time decreases."Answer 1 Question 22[select: , The student is incorrect; the correlation is r = 0.5 showing a moderate positive linear relationship; As sleep increases, reaction time increases., The student is incorrect; the relationship is actually strong negative, closer to r = -0.8. the verbal trend is still correct., The student is incorrect; while the correlation estimate of r = -0.5 and the strength/direction are correct, the verbal description is wrong; As sleep increases, reaction time increases.] Student B:"I examined a scatter plot comparing number of practice problems completed and math test score. I said the correlation was r = 0.3, showing a strong positive linear relationship. As practice increases, test scores increase."Answer 2 Question 22[select: , The student is incorrect; the direction of the trend is correct, but r = 0.3 reflects a weak, not strong, positive linear relationship., The student is correct; the graph supports a strong positive linear relationship, and the correlation of r = 0.3 is reasonable., The student is incorrect; the data shows no linear trend, so the correlation should be r = 0.] Student C:"I reviewed a scatter plot comparing outside temperature and electricity use in kilowatt-hours. I said the correlation was r = -0.6, showing a moderate negative linear relationship. As temperature increases, electricity use decreases."Answer 3 Question 22[select: , The student is incorrect; while the correlation estimate of r = -0.6 and the strength/direction are correct, the verbal description is wrong; As temperature increases, electricity use increases., The student is correct; all aspects of the interpretation are consistent with the graph., The student is incorrect; the graph shows a strong negative linear relationship, closer to r = -0.9. the verbal trend is accurate.]

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The prompt presents a scenario with three students, each describing a scatter plot and choosing a correlation r and a verbal trend. We will restate each student’s reasoning options and then analyze them. Student A: I looked at a scatter plot comparing hours of sleep per night and reaction time on a reflex test. I said the correlation was r = -0.5, indicating a moderate negative linear relationship. As sleep increases, reaction time decreases. - Answer 1 options for Student A: 1) The student is incorrect; the correlation is r = 0.5 showing a moderate positive linear relationship; As sleep increases, reaction time increases. 2) The student is incorrect; the relationship is actually strong negative, closer to r = -0.8. the verbal trend is still correct. 3) The student is incorrect; while the correlation estimate of r = -0.5 and the strength/direction are correct, the verbal description is wrong; As sleep increases, reaction time increases. Analysis for Student A: - Option 1 claims a moderate positive correlation (r ≈ 0.5) and that As sleep increases, reaction time increases. This contradicts the student’s stated r = -0.5, and the sign of the relationship. It also reverses the direction of the verbal trend, so it is inconsistent with the presented data and is incorrect. - Option 2 asserts a strong negative relationship with r ≈ -0.8 and that the verbal trend remains correct (As sleep increases, reaction time decreases). T......Login to view full explanation

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