AP Statistics free response: the new four-question format

The free-response section from May 2027

Source: AP Central exam and course revision pages, checked 7 October 2026. The four practices of the redesigned course are Formulate Questions, Collect Data, Analyze Data and Interpret Results.

What happened to the investigative task

Until the 2026 exam, the free-response section had six questions, the last of which was a longer investigative task that pushed students beyond the standard methods. From May 2027 that structure is replaced by four questions of 10 points each. College Board's revision notes say topics on investigative questions were added to the course itself, which fits the new first practice, Formulate Questions. In practice, this means students should expect to be asked what question a study could answer, how data should be collected, and what a result does and does not show, spread across the four questions rather than in one special task.

Older review books and past papers are still useful for inference, data description and study design, but students should skip topics the redesign removed and practice in the new 10-point format. Released materials for the new exam on AP Central are the best guide to the style.

Worked example 1: a hypothesis test, start to finish

A school wants to know whether more than half of its students support a later start time. In a random sample of 400 students, 248 say yes. Is there convincing evidence at the 0.05 level that more than half support the change?

1. State: H0: p = 0.5 and Ha: p > 0.5, where p is the proportion of all students at the school who support a later start.
2. Plan: one-sample z-test for a proportion. Conditions: the sample is random; 400 is less than 10% of the student population (state the assumption); expected counts 400 × 0.5 = 200 successes and 200 failures are both at least 10.
3. Do: p̂ = 248/400 = 0.62. z = (0.62 - 0.5) / sqrt(0.5 × 0.5 / 400) = 0.12 / 0.025 = 4.8. The p-value is P(Z ≥ 4.8), which is less than 0.0001.
4. Conclude: because the p-value is less than 0.05, we reject H0. There is convincing evidence that more than half of all students at the school support a later start time.
5. Points are lost for hypotheses without a defined parameter, conditions stated but not checked with numbers, and conclusions without context.

Worked example 2: a confidence interval and its meaning

Using the same sample, construct and interpret a 95% confidence interval for the proportion of students who support a later start.

1. Standard error: sqrt(0.62 × 0.38 / 400) = 0.0243.
2. Interval: 0.62 ± 1.96 × 0.0243 = 0.62 ± 0.048, so about (0.572, 0.668). Conditions as above, but check the large counts with the sample: 248 and 152 are both at least 10.
3. Interpretation: we are 95% confident that the interval from 0.572 to 0.668 captures the true proportion of all students at the school who support a later start.
4. Do not write '95% of students' or 'a 95% chance the proportion is in this interval'. The 95% describes the method: about 95% of intervals made this way capture the true proportion.

Worked example 3: describing a distribution

Commute times (minutes) for 11 students: 8, 10, 12, 12, 14, 15, 15, 17, 18, 22, 41. Describe the distribution.

1. Center: the median is 15 minutes. The mean is 184/11 = 16.7 minutes, pulled up by the large value.
2. Variability: Q1 = 12 and Q3 = 18, so the IQR is 6 minutes.
3. Outliers: the upper fence is 18 + 1.5 × 6 = 27, so 41 minutes is an outlier.
4. Shape: roughly symmetric apart from the outlier, which creates a long right tail.
5. Full credit needs all four (shape, center, variability, outliers) in the context of commute times.

Common mistakes

• No context: 'reject H0' with no mention of students or start times.
• Defining the parameter as the sample statistic (p̂) instead of the population proportion (p).
• Listing conditions without checking them against the numbers in the question.
• Interpreting a confidence level as a probability about one interval.
• Saying an observational study proves cause and effect. Only a randomized experiment supports a causal conclusion.
• Writing calculator syntax only. Show the formula or name the procedure and give the key values.

How one-to-one lessons help with AP Statistics FRQs

AP Statistics answers are graded on communication as much as on numbers, so students who are good at maths can still lose points. In lessons the tutor sets a 10-point question under time, then reviews the response line by line on the shared whiteboard, checking the parameter, the conditions, the calculation and the conclusion in context. Because the new exam is typed, practice should include typing answers clearly. The tutor also checks that the student is studying the redesigned five-unit course rather than removed topics.

With a new format in its first year, released sample questions on AP Central are limited, so tutors adapt older free-response questions to the new practices and point values.

Self-check

• Can you write hypotheses with a parameter defined in context?
• Can you check the random, 10% and large counts conditions with numbers?
• Can you interpret a 95% confidence interval correctly in one sentence?
• Can you describe a distribution with shape, center, variability and outliers in context?
• Can you explain why random assignment allows a cause-and-effect conclusion?