AP Statistics Scatterplots and Correlation Test Solutions and Scoring (PDF)

AP Statistics math test solutions: Scatterplots and Correlation – Maths PDF

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This scatterplots correlation test answers for AP Statistics covers scatterplots and correlation (Common Core AP STAT 2.4, AP STAT 2.5, HSS-ID.B.6, HSS-ID.C.8, HSS-ID.C.9), with a free PDF to print.

Each solution has a scoring guide. Give credit for the four parts of a scatterplot description, for correct arithmetic, and for explanations that mention context and the limits of correlation.

AP Statistics · Common Core State Standards: AP STAT 2.4, AP STAT 2.5, HSS-ID.B.6, HSS-ID.C.8, HSS-ID.C.9

Scatterplots correlation test answers: worked solutions

Question 1 – Describe a scatterplot [4 pts]

Minutes of practice and free throws made.

Direction: positive. Form: linear. Strength: strong (r = 0.951). Unusual features: none.

Positive, linear, strong association (r = 0.951), with no outliers: more practice goes with more free throws.

Scoring: 1 point each for direction, form, strength, and context/unusual features.

Question 2 – Compute r [3 pts]

z-scores of x: -1.265, -0.632, 0, 0.632, 1.265. z-scores of y: -1.433, -0.187, 0.125, 0.125, 1.371.

The sum of products divided by 4 gives r = 0.936.

r = 0.936.

Scoring: 1 point for z-scores, 1 point for the products and sum, 1 point for r.

Question 3 – Interpret and units [3 pts]

(a) Strong negative linear association: older cars tend to cost less.

(b) r stays -0.91.

Strong negative; unchanged; no.

Scoring: 1 point per part.

Question 4 – r and curved data [2 pts]

r measures only linear association.

The variables are strongly related in a curved way. A near-zero r only means no linear association.

Scoring: 1 point for linear-only, 1 point for noting the curved relationship.

Question 5 – Outlier effect [2 pts]

The point was far from the linear trend and weakened it.

Removing the outlier strengthens the linear pattern, so r increases. Correlation is not resistant.

Scoring: 1 point for identifying the outlier effect, 1 point for r not resistant.

Question 6 – Lurking variable [2 pts]

Fire size drives both the number of firefighters and the damage.

Fire size is a lurking variable.

Scoring: 1 point for rejecting causation, 1 point for naming the lurking variable.

Question 7 – Match plots [2 pts]

|r| values: 0.95, 0.2, 0, 0.7.

0, -0.2, -0.7, 0.95.

Scoring: 2 points for a correct order; 1 point if one pair is swapped.

Question 8 – Unusual point [2 pts]

A scatterplot with an unusual point.

The point (6, 14) is far above the pattern formed by the other points.

It lowers r because it lies away from the linear trend.

Scoring: 1 point for identifying (6, 14), 1 point for the effect on r.

Total score

Total

20 points

Key facts behind this scatterplots correlation test answers

Key facts

Explanatory variable on the x-axis, response variable on the y-axis.
Describe direction, form, strength, and unusual features in context.
-1 <= r <= 1; r near 0 means little linear association, not no association.
r is unitless, unchanged by swapping x and y or by linear changes of units, and not resistant.
Correlation does not imply causation; look for lurking variables.

How to use this scatterplots correlation test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All AP Statistics chapters: AP Statistics math.

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