AP · Analysis & Prediction

2024 AP AP Statistics Past Paper: Analysis & Answers

The 2024 AP Statistics Free-Response section provided a balanced and conceptually rigorous assessment across exploring data, experimental design, probability models, and inference. The paper placed high demands on full statistical communication, requiring clear parameter definitions in context, precise justification of sampling conditions (including pooling for proportions), and interpretation of novel skewness metrics in the Investigative Task.

Updated: 18 Aug 2026

Analysis Sample paper

Difficulty 3.4/5

Total marks

Duration

90 mins

Most tested

Probability Distributions and Categorical Data Inference

Paper breakdown

Section II Part A (Questions 1-5): 20 marks · 65 minsSection II Part B (Question 6: Investigative Task): 4 marks · 25 mins

Top chapters

Unit 4: Probability, Random Variables, and Probability Distributions · 5 marksUnit 6: Inference for Categorical Data: Proportions · 4 marksUnit 3: Collecting Data · 4 marksUnit 8: Inference for Categorical Data: Chi-Square · 3 marksUnit 1: Exploring One-Variable Data · 3 marks

Executive Overview & Difficulty Verdict

The 2024 AP Statistics Free-Response Section (Section II) presents a well-balanced yet exacting examination. With a global mean score of 2.96 across all candidates, the free-response questions highlighted clear distinctions between algorithmic calculator execution and deep conceptual communication. Questions 1 through 5 covered core curriculum staples, while Question 6 (Investigative Task) introduced Pearson's coefficient of skewness to assess how students apply sampling distribution theory to novel diagnostic metrics.

Where the Marks Are Distributed

Marks are evenly spread across six 4-point questions (24 points total):

Question 1 (Inference - Proportions): A complete two-sample \(z\)-test for a difference in proportions, heavily weighting parameter context and condition verification (pooling for expected counts).
Question 2 (Exploring Data): Construction and interpretation of segmented bar graphs and mosaic plots, distinguishing relative frequency from absolute counts.
Question 3 (Collecting Data): Differentiating observational studies from experiments, detailing a completely randomized design step-by-step, and scope of inference.
Question 4 (Probability & Discrete RVs): Geometric distribution calculations, standard deviation formulas, truncated random variables, and long-run interpretation of expected value.
Question 5 (Multi-Focus Probability & Chi-Square): Two-way table conditional probabilities alongside setup and conclusion for a Chi-Square test of independence.
Question 6 (Investigative Task): Inference identification, 1.5 \(\times\) IQR outlier boundaries, calculating Pearson's skewness \(\frac{3(\bar{x}-m)}{s}\), and evaluating the normality condition for small samples.

Examiner Pitfalls & Common Traps

The Chief Reader report highlighted recurring candidate weaknesses:

Definitive Language in Conclusions: Claiming that hypotheses were 'proven' or that there is 'no difference' rather than stating there is 'insufficient convincing evidence.'
Incomplete Random Assignment Descriptions: Omitting essential steps such as 'without replacement,' failing to mix slips of paper, or defining inadequate boundaries in random number generators.
Failing to Distinguish Proportions from Frequencies: Conflating bar widths/areas on mosaic plots with raw frequencies rather than relative frequencies.
Neglecting Long-Run Language: Interpreting expected values without explicitly referencing 'over many, many repetitions/trials in the long run.'

Forward Strategy & Prediction

With Units 6 and 8 appearing prominently after lighter coverage in recent administrations, students should anticipate a return to Quantitative Inference (Means / Paired t-tests, Unit 7) and Linear Regression Inference (Unit 9 slopes) in upcoming sittings. Mastery of exact condition verification and strict adherence to non-definitive statistical arguments remain the highest-leverage scoring habits.

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Charts

Marks by chapter

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Question type mix

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Standard Free-Response (Multi-part)20 marks · 5 questions
Investigative Task (Extended Application)4 marks · 1 questions

Mark accessibility

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75%within easy or medium reach

easy: 8 marksmedium: 10 markshard: 6 marks

Difficulty trend

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Command word frequency

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Skill weighting

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Study ROI

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Hypothesis Testing & Significance Test Conclusions

7 marks · Difficulty 2.5 · recurrence 100%

Probability Models (Geometric, Binomial & Discrete RVs)

5 marks · Difficulty 2.8 · recurrence 95%

Experimental Design & Random Assignment Protocol

4 marks · Difficulty 3 · recurrence 90%

Graphical Displays & Relative Frequencies

3 marks · Difficulty 2.2 · recurrence 85%

Investigative Task / Novel Statistic Interpretations

4 marks · Difficulty 4.2 · recurrence 100%

Time vs marks

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marksmins

Next-year prediction

Topics worth watching next year, with the reason shown directly below each bar.

Unit 7: Inference for Quantitative Data: Means (Two-Sample / Matched Pairs t-test)90%

While Unit 7 concepts were touched in Question 6, a full 4-step inference procedure for means was omitted in favour of proportions in 2024, making a full t-procedure very likely next year.

Unit 9: Inference for Quantitative Data: Slopes85%

Slope inference was absent from the 2024 FRQ after only carrying minimal weight in 2023. Regression t-tests and confidence intervals for beta are highly due for a dedicated FRQ appearance.

Unit 5: Sampling Distributions (Central Limit Theorem & Simulating Means)80%

Standalone sampling distribution questions combining CLT verification and standard error modeling were lightly represented in 2024.

Cumulative marks ladder

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Topic-year heatmap

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May 2023

May 2024

Unit 1: Exploring One-Variable Data

Unit 2: Exploring Two-Variable Data

2.5

Unit 3: Collecting Data

Unit 4: Probability, Random Variables, and Probability Distributions

Unit 5: Sampling Distributions

Unit 6: Inference for Categorical Data: Proportions

Unit 7: Inference for Quantitative Data: Means

Unit 8: Inference for Categorical Data: Chi-Square

Unit 9: Inference for Quantitative Data: Slopes

1.5

Examiner insights

Official report

Common pitfalls

Using definitive wording such as 'this proves the null hypothesis' or 'there is no association' rather than non-definitive phrasing ('convincing statistical evidence to reject H0').
Failing to state 'without replacement' or describe equal chance mechanisms when detailing randomized experimental assignments.
Providing naked calculator syntax (e.g. 1-VAR STATS or geompdf without labeled arguments) without showing formulas or explicit algebraic steps.
Omitting population parameters in hypotheses or defining parameters in terms of sample statistics (e.g., using p-hat instead of p).
Confusing relative frequencies (proportions) with absolute counts when interpreting mosaic plots and segmented bar graphs.

Misconceptions

Assuming expected values must be integers or rounding calculated discrete expected values to whole numbers.
Believing a Chi-Square test can prove causal dependence rather than solely establishing statistical association between categorical variables.
Applying multiplication rules for independent events to joint probabilities from two-way tables before establishing independence.
Assuming a large counts condition for proportions can be checked using sample sizes greater than 30 rather than np >= 10 and n(1-p) >= 10.

Where marks are lost

Question 1: Omitting group and population context when defining parameter subscripts, or failing to pool sample proportions when checking large counts.
Question 3: Missing essential random mechanism details (such as mixing slips or specifying the RNG integer range 1 to 70 without replacement).
Question 4: Miscalculating the truncated outcome probability P(Y=4) by omitting the scenario where no crystal is found in 4 trials.
Question 4: Forgetting to frame the interpretation of expected value as an average over many repeated trials in the long run.
Question 6: Placing the test point incorrectly on the skewness diagnostic chart or failing to connect the sample size requirement (n < 30) to the observed skewness.

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