2018 Ap Statistics Free Response Answers

The 2018 AP Statistics free response answers provide a valuable window into how the College Board evaluates students’ ability to collect, analyze, and interpret data under timed conditions. By reviewing the official scoring guidelines and sample responses, learners can see exactly what earns full credit, where partial points are awarded, and which common misconceptions cost students valuable marks. This article walks through each of the six free‑response questions from the 2018 exam, highlights the key concepts tested, breaks down the model solutions, and offers practical tips for avoiding pitfalls on future exams.

Overview of the 2018 AP Statistics Free‑Response Section

The free‑response portion of the AP Statistics exam consists of six questions, each worth a total of 9 points, for a maximum of 54 points. Questions are designed to assess four major skill areas:

1. Exploring data – graphical and numerical summaries.
2. Sampling and experimentation – design, bias, and randomization.
3. Anticipating patterns – probability models and sampling distributions.
4. Statistical inference – confidence intervals, hypothesis tests, and interpretation.

In 2018, the College Board emphasized real‑world contexts, ranging from school lunch programs to medical trials, requiring students to translate story problems into appropriate statistical procedures. The scoring rubrics reward correct setup, accurate calculations, clear communication, and justified conclusions Turns out it matters..

Question 1: Exploring Categorical Data

Prompt (summarized): A school surveyed 200 students about whether they ate lunch in the cafeteria (yes/no) and their grade level (9th, 10th, 11th, 12th). The two‑way table of counts was provided Worth keeping that in mind..

What the question tested:

• Constructing and interpreting a segmented bar chart.
• Calculating conditional proportions.
• Stating an appropriate conclusion about association between grade level and lunch location.

Model answer outline:

1. Graph (2 points) – Draw a segmented bar chart with grade levels on the x‑axis and proportions of “yes” and “no” stacked for each bar. Label axes and include a legend.
2. Conditional proportions (2 points) – Compute, for each grade, the proportion of students who ate lunch in the cafeteria (e.g., 9th grade: 48/50 = 0.96). Show work.
3. Interpretation (2 points) – Note that the proportion of cafeteria lunch‑eaters decreases steadily from 9th to 12th grade, suggesting a negative association between grade level and cafeteria use.
4. Justification (1 point) – Reference the observed trend in the conditional proportions or the visual pattern in the bar chart.
5. Conclusion (1 point) – State that there appears to be an association; older students are less likely to eat lunch in the cafeteria.

Common errors:

• Forgetting to label the bar chart axes or legend (loss of 1‑2 points).
• Calculating overall proportions instead of conditional ones.
• Stating “there is no association” without referencing the data.

Tip: When a two‑way table appears, always ask yourself, “What proportion of each row (or column) falls into each category?” That is the key to earning the conditional‑proportion points Practical, not theoretical..

Question 2: Designing an Experiment

Prompt (summarized): A researcher wants to test whether a new study‑skill workshop improves test scores. Fifty volunteers are available; the researcher can assign them to either the workshop or a control group that receives no workshop.

What the question tested:

• Identifying elements of a well‑designed experiment (random assignment, control, replication).
• Recognizing potential confounding variables.
• Suggesting a method to reduce bias.

Model answer outline:

1. Random assignment (2 points) – Explain that the 50 volunteers should be randomly assigned to the workshop (treatment) or control group to ensure groups are comparable.
2. Control group (2 points) – State that the control group receives no workshop (or a placebo workshop) to isolate the effect of the intervention.
3. Replication (1 point) – Note that each group should contain enough participants (e.g., 25 each) to allow detection of a difference.
4. Potential confound (1 point) – Mention that motivation or prior study habits could differ between groups if not randomized.
5. Bias reduction (1 point) – Suggest using a double‑blind design where neither participants nor outcome assessors know who received the workshop.
6. Conclusion (1 point) – Summarize that random assignment, a control condition, and replication together support a causal inference about the workshop’s effect.

Common errors:

• Describing an observational study instead of an experiment.
• Forgetting to mention replication or sample size justification.
• Suggesting blinding without explaining who would be blinded.

Tip: When asked to “design an experiment,” always hit the three pillars: randomization, control, and replication. Then address any ethical or practical concerns (blinding, confounding).

Question 3: Probability and Random Variables

Prompt (summarized): A game consists of rolling a fair six‑sided die. If the result is 1 or 2, you win $3; if the result is 3, 4, or 5, you win $1; if the result is 6, you lose $2. Let X be the net winnings from one play Nothing fancy..

What the question tested:

• Building a probability distribution for a discrete random variable.
• Calculating the expected value (mean) and standard deviation.
• Interpreting the expected value in context.

Model answer outline:

1. Probability table (2 points) – List outcomes:
   • X = $3 with P = 2/6 = 1/3
   • X = $1 with P = 3/6 = 1/2
   • X = –$2 with P = 1/6
2. Expected value (2 points) – E[X] = (3)(1/3) + (1)(1/2) + (–2)(1/6) = 1 + 0.5 – 0.333… = 1.1667 ≈ $1.17. Show each term.
3. Variance and standard deviation (2 points) – Compute E[X²] then Var(X) = E[X²] – (E[X])²,