AP Stats · Unit 2 Progress Check

AP Statistics Unit 2 Progress Check: Probability, Random Variables, and Probability Distributions

AP Statistics Unit 2 is probability, random variables and probability distributions, and the Unit 2 Progress Check MCQ runs to about 42 questions with two free-response questions alongside. That is College Board’s current framework, effective for the 2026-27 school year. If you were told Unit 2 is two-variable data, that material is now Unit 5, and it is further down this page. We explain the reasoning; we never publish AP Classroom answer keys.

Updated September 2026Written by Mahmudul HasanFree · No signup

Every unit for this subject sits on the ap statistics progress check answers hub.

What Unit 2 covers

Twelve topics, grouped here into seven ideas, running from two-way tables to the central limit theorem. That last one is why the unit carries the weight it does: almost everything in Units 3 and 4 rests on it.

College Board weights Unit 2 at 15–25% of the multiple-choice section across roughly 24 class periods. Read that scope carefully. The weighting is for Section I only, and College Board publishes no unit weighting at all for the free-response section.

Two-way tables (2.1–2.2)

Joint, marginal and conditional relative frequencies read off a single table. A joint frequency divides by the grand total; a conditional divides by one row or column total. Choosing the wrong denominator is the most common error here, and this is where College Board now starts probability.

Simulation (2.3)

Estimating a probability by running many trials instead of computing it. A complete answer describes one trial, says what counts as a success, and gives the number of repetitions.

Probability rules (2.4–2.7)

Complements, unions, intersections, conditional probability and independence. Mutually exclusive is a claim about whether two events can happen together; independent is a claim about whether one changes the other’s probability. Two events that are mutually exclusive and both possible can never be independent, because once one has happened the other has probability zero.

Random variables (2.8–2.9)

A discrete probability distribution lists the values and their probabilities. The mean is a long-run average and often is not a value you could actually observe. College Board expects both the mean and the standard deviation to be interpreted with units and in the context of the situation.

The binomial distribution (2.10)

A fixed number of trials, two outcomes, a constant probability, and independent trials. Miss any one of those four and the binomial model does not apply. Mean np, standard deviation the square root of np(1−p).

The normal distribution (2.11)

Probability is area under the curve and the total area is 1. The empirical rule, which College Board also calls the 68–95–99.7 rule, covers one, two and three standard deviations. Boundaries come either from technology or from z-scores and a standard normal table.

Sampling distributions and the CLT (2.12)

The distribution of a statistic across all samples of a given size. The central limit theorem says the sampling distribution of a sample mean has a shape that a normal distribution approximates, and that the larger the sample, the better that approximation gets. College Board also names the randomization distribution here, built by repeatedly reallocating responses to treatment groups.

A population that is strongly right-skewed still produces a nearly symmetric distribution of sample means, and the bigger the sample the closer it gets. Drawn from the exact distributions rather than a sketch.

What is on the Unit 2 Progress Check MCQ

College Board publishes the size of every Progress Check, in the Course at a Glance and again on the Unit 2 opener of the Course and Exam Description. The Unit 2 Progress Check is about 42 multiple-choice questions and 2 free-response questions.

One coincidence is worth naming before it misleads you. The AP Statistics exam also has 42 multiple-choice questions. The two numbers are unrelated: a Progress Check is a formative check on one unit, and the exam samples all five.

Progress Check	Multiple-choice	Free-response
Unit 1: Exploring One-Variable Data and Collecting Data	about 44	3
Unit 2: Probability, Random Variables, and Probability Distributions	about 42	2
Unit 3: Inference for Categorical Data: Proportions	about 65	3
Unit 4: Inference for Quantitative Data: Means	about 49	3
Unit 5: Regression Analysis	about 19	2

Unit 3 is by far the longest and Unit 5 the shortest, which is worth knowing when you are deciding how much of a week to give each one.

The question types that recur

Probability questions come in a handful of recognizable shapes. Working out which shape you are looking at is most of the work.

Conditional probability from a two-way table

You are handed a table and asked for the probability of one thing given another. The word given tells you which total belongs on the bottom. If the question restricts you to a row, the row total is the denominator, not the grand total, and reading straight off the grand total is the fastest way to lose the question.

Mutually exclusive versus independent

The question usually gives you two of P(A), P(B) and P(A and B) and asks which property holds. Test them separately: mutually exclusive means P(A and B) is zero, independent means P(A and B) equals P(A) times P(B). Answering from intuition rather than the arithmetic is where this one goes wrong.

Expected value in context

A distribution is given and you are asked for the mean, or for a decision based on it. Multiply each value by its probability and add, then say what the number means for the situation described. A bare number rarely earns full credit.

Binomial conditions

Often the question is not the calculation but whether the binomial model applies at all. Check the fixed number of trials, the two outcomes, the constant probability and the independence. Sampling without replacement from a small population breaks the last two.

Normal areas and boundaries

Either an area from an interval, or an interval from an area. Sketch the curve, shade what you are after, and note whether you are working inward from a percentage or outward from a value. The empirical rule handles the tidy cases without any technology at all.

Sampling distribution shape

You are shown a skewed population and asked what the distribution of the sample mean looks like. The answer depends on the sample size, not on the shape of the population, which is exactly the point the central limit theorem is making.

The two free-response questions

College Board lists both Unit 2 Progress Check free-response questions as Multi-Focus on Practices 3 and 4. Practice 3 is Analyze Data: constructing representations and calculating statistics, probabilities and parameters. Practice 4 is Interpret Results: describing distributions, interpreting what a calculation means, and justifying a claim from it.

That pairing tells you what these questions will not be. Neither is a full inference write-up, because inference is assessed under Practices 2, 3 and 4 and is Question 3 on the exam. Expect calculation followed by interpretation in context, and expect the interpretation to carry real credit rather than being a formality after the arithmetic.

The same pairing appears on the exam as Question 2, one of four free-response questions worth 10 points each and 12.5% of the score each.

Where students lose the most points

Dividing by the wrong total

Conditional probability restricts you to part of the table. If the question says given that a student plays a sport, every probability after that lives inside the sport row, and the grand total stops being relevant.

Treating mutually exclusive as independent

They sound similar and they are close to opposites. If two events cannot happen together and both have non-zero probability, then knowing one happened tells you the other did not, which is the strongest possible dependence.

Reading the mean of a random variable as a likely outcome

An expected value of 2.4 children does not mean any family has 2.4 children. It is what the average settles to over a very large number of repetitions, and saying so is usually part of the credit.

Using the binomial formula without checking its conditions

The arithmetic works on any numbers you feed it, which is the problem. Confirm the four conditions before you start, because a question that breaks one of them is testing whether you noticed.

Interpreting a probability without context or units

College Board is explicit that a complete interpretation includes context and units. A correct number with no sentence attached is an incomplete answer, and this is the cheapest credit on the paper.

Confusing the distribution of the data with the distribution of a statistic

A sampling distribution is not the distribution of one sample. It is the distribution of a statistic across every sample of that size, and the two have different shapes and very different spreads.

If you were told Unit 2 is two-variable data

College Board revised AP Statistics for the 2026-27 school year. The old Unit 9, Inference for Quantitative Data: Slopes, was removed outright, and College Board describes what remained as Units 1 to 8 being consolidated into 5. A course that had nine units now has five, and almost every unit number moved with it.

Scatterplots, correlation, least-squares regression, residuals and r-squared are now Unit 5, Regression Analysis, weighted at 10–20% of the multiple-choice section across about 9 class periods. Its Progress Check is the smallest of the five, at roughly 19 multiple-choice questions and 2 free-response questions. The material itself is almost all still examinable, so here it is.

Describing a scatterplot

Form, direction, strength and unusual features, in that order. College Board’s term is unusual features, meaning clusters and points that do not fit the general pattern.

Correlation r

Unit-free and always between −1 and 1 inclusive, and it measures linear association only. A correlation near zero means weak linear association, not no relationship: a strongly curved pattern can sit at r near zero and still be tight.

The least-squares line

The predicted value, written y-hat, is a + bx. Interpret the slope as the predicted change in the response for a one-unit increase in the explanatory variable, and name both variables and their units when you do.

Residuals and residual plots

A residual is observed minus predicted. Curvature in the residual plot says the linear model is not the right one; apparent randomness supports the model. Judge fit from the plot rather than from r alone.

r-squared

The proportion of the variation in the response variable that the linear model explains. The model does the explaining, not the explanatory variable on its own, and the value sits between 0 and 1.

Extrapolation and interpolation

Predicting inside the observed range of x is interpolation; predicting outside it is extrapolation, and the prediction gets less reliable the further out you go.

Two details inside that material also changed, and both catch people out. College Board removed the topic on analyzing departures from linearity, and the terms influential point and leverage appear nowhere in the current course framework; what survives is unusual features. Separately, the formula sheet now gives you the least-squares line but no longer gives you a formula for r or for the slope, so those are no longer handed to you on exam day. Our AP Statistics formula sheet and tables page has the current list.

The exam changed alongside the course. Multiple choice went from 40 questions to 42 and from five answer choices to four. Free response went from six questions worth 4 points each to four worth 10 points each, and the Investigative Task was removed. Other topics dropped from the course are combining random variables, the geometric distribution and the chi-square goodness-of-fit test. From May 2027 the exam is fully digital in Bluebook with no paper free-response booklet, though you still get scratch paper and a printed reference information booklet. The next exam is Tuesday 11 May 2027. All of that is set out on College Board’s AP Statistics revisions page.

How to see your own Unit 2 Progress Check answers

We do not publish answer keys, and the honest reason is that you should not need ours. College Board builds the explanation into AP Classroom itself.

The Course and Exam Description describes Progress Checks as free formative assessments, delivered with multiple-choice questions that carry rationales explaining the correct and the incorrect answers, and free-response questions that carry scoring information. College Board’s own instruction to teachers is to give question-level feedback through those rationales, and it notes that students can view their own progress over time.

So the answers you want already exist, inside the platform, written by the people who wrote the questions. Your teacher decides when they are released. If you cannot see them yet, that is the thing to ask for, and it is a reasonable thing to ask for. A scoring guide someone uploaded to a file-sharing site gives you a letter; the rationale tells you why the other three were wrong, which is the part that changes your next score.

How to work through this unit

Start with the two-way table topics even though they look like leftovers from Unit 1. College Board put them at the front of Unit 2 deliberately, because conditional relative frequency and conditional probability are the same idea in two notations. It is an easy bridge to skip, and skipping it makes the rest of the unit harder than it needs to be.

Then work outward from the definitions rather than the formulas. Nearly every mistake in the list above is a modeling mistake rather than an arithmetic one: the wrong denominator, the wrong distribution, the right number with no sentence attached.

One thing not to do with your result: a Progress Check score is not an exam score. College Board calls these assessments formative and publishes no 1–5 scale for them, so there is nothing to convert. When you do want to see how a raw score maps onto 1 to 5, our AP Stats exam score calculator models the real exam, with its 42 multiple-choice questions and four 10-point free-response questions, and the AP Statistics Review covers the full format and a study plan.

Frequently asked questions

Quick answers, checked against College Board.

Is AP Statistics Unit 2 still two-variable data?

No. College Board revised the course for the 2026-27 school year and Unit 2 is now Probability, Random Variables, and Probability Distributions. Scatterplots, correlation and least-squares regression moved to Unit 5, Regression Analysis.

How many questions are on the AP Statistics Unit 2 Progress Check?

College Board publishes about 42 multiple-choice questions and 2 free-response questions. For comparison, Unit 3 is the longest at about 65 and Unit 5 the shortest at about 19.

Does a Progress Check score predict my AP score?

No. College Board calls Progress Checks formative and publishes no 1 to 5 scale for them. They show you which topics to go back to; they do not forecast a May result.

Is the geometric distribution still in AP Statistics?

No. College Board removed it in the 2026 revision, along with combining random variables, the chi-square goodness-of-fit test, analyzing departures from linearity, and the whole of the old Unit 9 on inference for slopes.

Do you post AP Statistics Unit 2 answer keys?

No. AP Classroom work is graded as your own work, so we publish the reasoning instead. AP Classroom carries rationales for the correct and the incorrect answers once your teacher releases them.