AP Statistics review and study guide

By Ashraf Bhura, Co-Founder, STEM-Tutor · Updated October 2026

A focused AP Statistics review covers the big ideas, a reliable routine for inference, and plenty of practice explaining answers in context.

The big ideas to review

• Variation: data vary, and statistics vary from sample to sample.
• Patterns and uncertainty: describing distributions and relationships.
• Data collection: what a study's design lets you conclude.
• Inference: using samples to make claims about populations, with stated uncertainty.

A routine for every inference question

1. State: the parameter and the hypotheses or the confidence level, in context.
2. Plan: name the procedure and check the conditions.
3. Do: calculate the test statistic and p-value, or the interval.
4. Conclude: answer the question in context.

Free-response tips

• Answer exactly what is asked, using the words from the question.
• Show your method: name procedures and formulas, not just calculator output.
• Keep conclusions linked to the p-value and the significance level.
• For the longer investigative task, read every part first; later parts often build on earlier ones.

A plan for the final month

• Week 1: exploring data, regression and study design.
• Week 2: probability, random variables and sampling distributions.
• Week 3: all inference procedures, side by side.
• Week 4: full timed practice exams and targeted review.

Use the official practice materials and scoring guidelines on AP Central, and keep our formula sheet guide open while you practise.

A topic-by-topic review checklist

Exploring data

• Describe a distribution with shape, centre, spread and outliers, in context.
• Compare two distributions using comparative language, such as "greater than" or "about the same as".
• Interpret slope, intercept, r and r² for a regression line, and use residual plots to judge whether a linear model fits.

Collecting data

• Name sampling methods and sources of bias.
• Explain why random assignment allows causal conclusions and random sampling allows generalisation.
• Identify confounding variables and the purpose of blocking.

Probability

• Use the addition and multiplication rules, two-way tables and tree diagrams.
• Calculate expected value and standard deviation of random variables.
• Recognise binomial and geometric settings.

Inference

• Choose the right procedure, check its conditions and interpret results in context.
• Interpret a confidence level and a p-value correctly.
• Explain Type I and Type II errors and power in context.

A free-response question, answered

Question: A random sample of 50 batteries has mean life 102 hours and standard deviation 10 hours. Is there evidence the mean life exceeds 100 hours?

1. State: μ = true mean battery life. H₀: μ = 100; H_a: μ > 100; α = 0.05.
2. Plan: one-sample t test. Random sample; 50 batteries is less than 10% of all batteries; n = 50 is large enough for the central limit theorem.
3. Do: t = (102 − 100)/(10/√50) ≈ 1.41, with 49 degrees of freedom; p-value ≈ 0.08.
4. Conclude: Because 0.08 > 0.05, we fail to reject H₀. There is not convincing evidence that the mean battery life exceeds 100 hours.

Practice questions

Try each one before opening the answer.

Frequently asked questions

What are the most common free-response question types?

Exploring data, study design, probability, inference and a longer investigative task that combines ideas.

How do I improve my communication?

Copy the structure of top-scoring answers from released scoring guidelines, and always end with a sentence in context.

Key takeaways

• Review by big idea: exploring data, collecting data, probability, inference.
• Use the four-step routine for every inference question.
• Interpret confidence levels, p-values and errors carefully.
• Practise the investigative task under timed conditions.
• Mark practice answers with official scoring guidelines.

Where to go next

Use these guides alongside your review.

• AP Statistics formula sheet, explained
• Hypothesis testing, step by step
• AP Statistics units, explained

How to use practice exams well

A practice exam is only useful if you learn from it. After each one, sort every lost point into one of three groups: a concept you did not understand, a procedure you chose wrongly, or a communication slip, such as a missing context sentence. Each group needs a different fix. Concepts need re-learning, procedure choice needs mixed practice, and communication needs comparing your wording with scoring guidelines.

The investigative task

One free-response question is longer and asks you to apply ideas to an unfamiliar situation. It often combines several units, for example a probability calculation feeding into a simulation, or a new statistic you have not seen before. Read every part first, notice how they build on each other, and do not panic if the setting is new: the underlying skills are the same ones you have practised all year.

Calculator fluency

Know how to enter data in lists, get one- and two-variable statistics, find normal and binomial probabilities, and run each inference procedure. Then practise writing the results by hand: name the procedure, give the test statistic, degrees of freedom where relevant, and the p-value or interval.

The night before

• Re-read your one-page summaries of conditions for each procedure.
• Check your calculator's batteries and mode settings.
• Get a full night's sleep. Careful reading is worth more than last-minute cramming.

More practice

Try each one before opening the answer.

One more worked example: expected value

A game costs $2 to play. You win $10 with probability 0.1 and nothing otherwise. What is your expected gain per game?

• Net outcomes: +$8 with probability 0.1, and −$2 with probability 0.9.
• Expected value = 8 × 0.1 + (−2) × 0.9 = 0.8 − 1.8 = −$1.00.
• On average you lose $1 per game in the long run, even though you sometimes win.

More questions students ask

Should I memorise the formula sheet?

No, you get it in the exam. Know what each formula means and when to use it.

Quick check

Study tip

Keep a list of the exact phrases from scoring guidelines that earned full credit, and reuse them in your own answers.

A final word

Review is most effective when it is active. Rather than rereading notes, answer questions, mark them honestly and fix every mistake. A few weeks of this steady routine usually improves scores far more than long last-minute sessions. Keep your sessions short, regular and focused on your weakest topics, and track your progress.