AP Statistics units, explained

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

AP Statistics is organised into nine units, moving from describing data to drawing conclusions from it. Here is what each covers.

The nine units

1. Exploring One-Variable Data: graphs, centre, spread, shape and the normal distribution.
2. Exploring Two-Variable Data: scatterplots, correlation, least-squares regression and residuals.
3. Collecting Data: sampling methods, bias, observational studies and experiments.
4. Probability, Random Variables, and Probability Distributions: probability rules, expected value, binomial and geometric distributions.
5. Sampling Distributions: how statistics vary from sample to sample, and the central limit theorem.
6. Inference for Categorical Data: Proportions: confidence intervals and significance tests for proportions.
7. Inference for Quantitative Data: Means: t procedures for one sample, two samples and paired data.
8. Inference for Categorical Data: Chi-Square: goodness-of-fit, homogeneity and independence tests.
9. Inference for Quantitative Data: Slopes: inference about the slope of a regression line.

Unit weightings and exam details are in the course and exam description on AP Central.

What to focus on in each stage

• Units 1 and 2: describe data in context, always mentioning shape, centre, spread and unusual features.
• Unit 3: know exactly why random assignment allows cause-and-effect conclusions and random sampling allows generalisation.
• Units 4 and 5: build intuition for variability. This is the foundation for all inference.
• Units 6 to 9: master one inference routine and apply it to every procedure.

The most common mistakes

• Describing data without context.
• Confusing a sample statistic with a population parameter.
• Skipping condition checks.
• Interpreting a confidence level as the probability that the parameter is in a specific interval.

A worked example from every unit

Unit 1: describing data

Test scores have a median of 72 and an IQR of 15, with a long tail to the right. Which measures should you report?

• The distribution is skewed right, so the median and IQR describe it best; they are resistant to the long tail.

Unit 2: a residual

The regression line is ŷ = 40 + 6x. A student who studied 5 hours scored 74. Find the residual.

• Predicted score: 40 + 6 × 5 = 70.
• Residual = observed − predicted = 74 − 70 = 4. The line underpredicted this student by 4 points.

Unit 3: study design

A researcher surveys 500 randomly chosen adults about exercise and stress. Can she conclude exercise reduces stress?

• This is an observational study, so it shows association only. No causal conclusion; a randomised experiment would be needed.

Unit 4: probability rules

P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.2. Find P(A or B).

• P(A or B) = 0.5 + 0.4 − 0.2 = 0.7.

Unit 5: a sampling distribution

The true proportion is p = 0.3 and samples have n = 100. Describe the sampling distribution of p̂.

• Mean 0.3, standard deviation √(0.3 × 0.7/100) ≈ 0.046, approximately normal because np = 30 and n(1 − p) = 70 are both at least 10.

Unit 7: a t interval

A sample of 16 has mean 72 and standard deviation 8. Build a 95% confidence interval for the mean (t* = 2.131 with 15 degrees of freedom).

• Standard error = 8/√16 = 2.
• 72 ± 2.131 × 2 = 72 ± 4.26, so (67.74, 76.26).

Unit 8: chi-square degrees of freedom

A test of independence uses a 3 × 4 table. How many degrees of freedom?

• (3 − 1)(4 − 1) = 6.

Unit 9: inference for slope

A regression gives slope b = 1.2 with standard error 0.4. Find the test statistic for H₀: β = 0.

• t = (1.2 − 0)/0.4 = 3.0, with n − 2 degrees of freedom.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Which units carry the most weight?

Check the current course and exam description on AP Central. Inference units together make up a large share of the exam.

In what order should I review?

Follow the course order once, then mix units in timed practice, because the exam mixes them.

Key takeaways

• Units 1 to 3 describe data and how it was collected.
• Units 4 and 5 build probability and the idea of sampling variability.
• Units 6 to 9 are inference for proportions, means, counts and slopes.
• Study design decides what you can conclude.
• Use one routine for every inference procedure.

Where to go next

Go deeper on the units that matter most.

• AP Statistics Unit 1
• Hypothesis testing, step by step
• AP Statistics review and study guide

How the units build on each other

The course moves from describing data you have, to thinking about data you could have collected, to drawing conclusions about a whole population. Units 1 and 2 teach you to summarise and display data. Unit 3 explains how the way data is collected limits what you can conclude. Units 4 and 5 build the probability and sampling ideas that make inference possible. Units 6 to 9 then use those ideas to estimate and test claims about proportions, means, counts in categories and regression slopes.

When reviewing, follow that story. If inference feels confusing, the cause is often a gap in sampling distributions from Unit 5, so start there.

One more worked example: Unit 6 confidence interval

In a random sample of 250 voters, 140 support a new park. Build a 95% confidence interval for the true proportion of supporters.

• p̂ = 140/250 = 0.56. Conditions: random sample, less than 10% of all voters, and 140 and 110 are both at least 10.
• Standard error = √(0.56 × 0.44/250) ≈ 0.0314.
• Interval: 0.56 ± 1.96 × 0.0314 = 0.56 ± 0.062, so (0.498, 0.622).
• Because 0.5 is just inside the interval, the data do not give convincing evidence that a majority supports the park.

More questions students ask

Is regression only in Unit 2?

Regression is introduced in Unit 2 and returns in Unit 9, where you make inferences about the slope.

Quick check

Study tip

At the end of each unit, write one exam-style question on it for a friend, and answer theirs. Writing questions shows you what really matters in a unit.

A final word

Treat the nine units as one connected course rather than separate topics. When you can explain how sampling distributions in Unit 5 make the confidence intervals and tests in Units 6 to 9 possible, you understand the heart of AP Statistics, and the rest becomes much easier to remember. Revisit Unit 5 whenever inference starts to feel confusing.