Graphical Representations Between Two Quantitative Variables
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalA scatterplot shows two quantitative variables on the same individuals, with the explanatory variable on the horizontal axis and the response on the vertical. A complete description covers four features in context: form (linear, curved, or none), direction (positive or negative), strength (how tightly the points cluster), and unusual features (outliers, clusters, gaps). For weekly study hours against exam score: the association is positive, linear, and strong, with no apparent outliers, and students who study more tend to score higher.
Descriptions arrive with one feature instead of four, usually direction alone, and with no variable named, which makes them templates rather than descriptions of these data. Form gets justified by the fact that a line can be drawn through the cloud, when a line can be drawn through anything and the question is whether the points bend systematically. Strength gets reported without saying strong what, though a tight curve and a loose straight band are different findings. And unusual points get deleted rather than investigated and described.
The work
3 ways in · any order
Lesson
Graphical Representations Between Two Quantitative Variables
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Sets up scatterplots with the explanatory variable on the horizontal axis, then makes description a four-item checklist: form justified by whether the points bend, direction, strength, and unusual features, each stated with the variables named.
Diagnostic
10-item topic check
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Ten items on describing scatterplots: one feature offered instead of four, linear justified by drawing a line, strength reported without form, axes swapped, and unusual points deleted. Take it cold to find your habit, or after the lesson to check it is gone.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.