Mathfolis

Scatterplots

Unit 2 · Exploring Two-Variable Data

What AP Stats asks here

A scatterplot displays two quantitative variables jointly, one point per observation. The mandatory description framework is FDSO — Form, Direction, Strength, Outliers — in context. Two recurring AP traps: (1) calling a curved pattern 'strong' without naming the form first, and (2) computing rr or fitting an LSRL before looking at the scatterplot.

FDSO description

Form
linear, curved, or no pattern\text{linear, curved, or no pattern}
Direction
positive or negative\text{positive or negative}
Strength
tightness of points around the named form\text{tightness of points around the named form}
Outliers
points away from the overall pattern\text{points away from the overall pattern}

Variable roles

Explanatory (x-axis)
predictor or hypothesized cause\text{predictor or hypothesized cause}
Response (y-axis)
outcome being explained\text{outcome being explained}
AP Tip: Always plot the scatterplot first. The correlation r and the LSRL slope are summaries of a linear pattern; if the data is curved, those summaries are misleading even when computed correctly.
Caution: Strength is relative to the named form. A tight parabola is a 'strong curvilinear' pattern, not 'strong' on its own. Reporting 'strong' without form invites a linear misreading.
Type 1

Explanatory vs response variable

The explanatory variable is the predictor (x); the response is the outcome (y). The choice follows from the research question, not from when each variable was measured.

Example 1
Researchers want to predict adult income from years of education. Which assignment is correct? (A) x = adult income; y = years of education (B) x = years of education; y = adult income (C) Either axis is fine — correlation is symmetric. (D) Cannot tell without seeing the data.

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Type 2

FDSO description

Pick the choice that names form first, then direction, then strength, then any outliers — all tied to context. Vague descriptions lose AP credit.

Example 2
A scatterplot of hours studied (x) vs exam score (y) for 30 students has points clustering tightly along an upward-sloping line, with one student at (2 hr, 95). Which is the best FDSO description? (A) Positive correlation, very strong. (B) Strong, positive, linear association; one outlier at (2 hr, 95) — unusual high score for low study time. (C) Linear pattern with no outliers. (D) Negative association because the outlier reduces overall score.

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Type 3

Specify form before strength

Strength alone is ambiguous. Always name the form first, then qualify strength relative to that form.

Example 3
A student looks at a tightly clustered parabolic (U-shaped) cloud and reports 'strong relationship'. Which critique is correct? (A) The description is fine — 'strong' implies any kind of pattern. (B) 'Strong' needs a form before it. The correct description is 'strong curvilinear relationship', because rr would underreport the strength of a non-linear pattern. (C) Strength is not a defined property of scatterplots. (D) The relationship is weak because rr is near 0.

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