Free Practice Test: AP Statistics

Last updated: August 16, 2026

Start free practice exam →

AP exams let you earn college credit, test out of an intro-level class, or both, while showing college admissions officers you can handle rigorous coursework. Most colleges and universities in the US recognize AP credit for a strong score.
AP Statistics is less about pure computation and more about reasoning: interpreting data, designing studies, and drawing conclusions while accounting for uncertainty. It's arguably the most "verbal" of the AP math and science exams, since a huge share of your points come from explaining your reasoning in words, not just producing a correct number.

Fast Statistics Study Guide

The AP Statistics exam runs about 3 hours. Section I is 40 multiple-choice questions in 90 minutes. Section II is 6 free-response questions in 90 minutes: five shorter, targeted questions and one longer Investigative Task that asks you to apply statistical reasoning to a novel scenario you haven't seen a template for before. A graphing calculator with statistical capabilities is required for the entire exam, and you'll also receive a formula sheet and standard normal (z) table. Multiple-choice and free-response sections are weighted equally toward your final score of 1 to 5. Confirm exact timing and the approved calculator list against the current AP Course and Exam Description before test day.

Exploring Data: One and Two Variables (25–30% combined)

The course opens with descriptive statistics: measures of center (mean, median) and spread (range, IQR, standard deviation), and how to describe a distribution's shape, center, and spread from a histogram, boxplot, or dotplot. Two-variable data introduces scatterplots, correlation, and linear regression, including how to interpret the slope and y-intercept of a regression line in context and how to identify outliers and influential points. Being able to describe data in full sentences, not just compute a number, is tested constantly here.

Collecting Data (12–15%)

This unit covers the difference between an observational study (which can show association) and a controlled experiment (which can show causation), and why that distinction matters so much for what conclusions you're allowed to draw. You'll need sampling methods (simple random, stratified, cluster, systematic) and their sources of bias, plus experimental design principles like control groups, randomization, replication, and blocking. This is a reliable source of free-response points because the reasoning is conceptual rather than computational.

Probability and Random Variables (18–20% combined)

Covers basic probability rules (addition rule, multiplication rule, conditional probability), and how to build and interpret a probability distribution for a discrete random variable, including calculating its mean (expected value) and standard deviation. The binomial and geometric distributions are named, testable distributions with their own formulas you're expected to apply. The normal distribution and how to use z-scores to find probabilities also live in this stretch of the course.

Sampling Distributions (7–12%)

This is the conceptual bridge to inference, and one of the trickiest units for most students. A sampling distribution describes how a statistic (like a sample mean or sample proportion) would vary across many different random samples of the same size. The Central Limit Theorem (which explains why sampling distributions of the mean tend toward a normal shape as sample size grows, even when the underlying population isn't normal) is the single most important idea in this unit and underlies everything in the inference units that follow.

Statistical Inference (34–44% combined)

The largest share of the course, spanning four units: inference for a single proportion, inference for means (including the t-distribution for small samples), inference for categorical data using chi-square tests, and inference for the slope of a regression line. Every inference procedure follows the same basic logic: state a hypothesis, check conditions, compute a test statistic and p-value, and state a conclusion in context. The free-response section rewards students who can execute that full sequence cleanly and explain what the result actually means in plain language.

Statistics Free Practice Test

So, are you ready to test the waters? Take this practice quiz and judge your preparation level before diving into deeper study. AP test questions cover a mix of multiple-choice questions and free-response questions. The following are original sample questions, written by Powerhouse Prep, in the style of the types of questions that may appear on the exam.

Question 1: A dataset's distribution is strongly right-skewed with a few very high outliers. Which measure of center and spread would be most appropriate to report?

  1. Mean and standard deviation
  2. Median and interquartile range (IQR)
  3. Mode and range
  4. Mean and range

Correct Answer: B. Median and interquartile range (IQR)

Explanation: The mean and standard deviation are both sensitive to outliers and skew, since every value in the dataset (including extreme ones) contributes directly to their calculation. The median and IQR are resistant measures: they're based on the position of values in the ordered dataset, not their exact magnitude, so a few extreme outliers won't drag them around the way they would the mean. For a strongly skewed distribution, median and IQR give a more representative picture.


Question 2: A researcher wants to know whether a new fertilizer increases crop yield. She randomly assigns half of 40 similar plots of land to receive the fertilizer and half to receive no fertilizer, then compares average yield. This study design allows her to conclude:

  1. Correlation only, not causation, because it's an observational study
  2. Causation, because random assignment to treatment and control groups was used
  3. Nothing meaningful, because the sample size is too small to draw any conclusion
  4. Causation, but only if she also used a stratified random sample

Correct Answer: B. Causation, because random assignment to treatment and control groups was used

Explanation: This is a controlled experiment, not an observational study, because the researcher actively assigns the treatment (fertilizer or none) rather than simply observing existing conditions. Random assignment to treatment and control groups is what allows a well-designed experiment to support a causal conclusion, since it balances out other confounding variables between the two groups on average.


Question 3: According to the Central Limit Theorem, as sample size increases, the sampling distribution of the sample mean:

  1. Becomes more skewed, regardless of the shape of the population distribution
  2. Approaches a normal distribution, regardless of the shape of the population distribution, and its standard deviation decreases
  3. Stays exactly the same shape as the population distribution
  4. Becomes impossible to predict

Correct Answer: B. Approaches a normal distribution, regardless of the shape of the population distribution, and its standard deviation decreases

Explanation: The Central Limit Theorem states that as sample size increases, the sampling distribution of the sample mean approaches a normal distribution regardless of the shape of the underlying population, even if the population itself is skewed. At the same time, the standard deviation of the sampling distribution (called the standard error) shrinks as sample size grows, since larger samples give more precise estimates of the true population mean.


Question 4: In a hypothesis test, a p-value of 0.03 is obtained, and the significance level was set at α = 0.05 before the test. What is the correct conclusion?

  1. Fail to reject the null hypothesis, since 0.03 is a small number
  2. Reject the null hypothesis, since the p-value is less than the significance level
  3. Accept the alternative hypothesis as proven true with certainty
  4. The test is inconclusive because the p-value is close to the significance level

Correct Answer: B. Reject the null hypothesis, since the p-value is less than the significance level

Explanation: The decision rule in hypothesis testing is to reject the null hypothesis when the p-value is less than the pre-set significance level. Here, 0.03 < 0.05, so the null hypothesis is rejected in favor of the alternative. It's important not to overstate the conclusion, though: rejecting the null provides statistical evidence for the alternative, but it never 'proves' anything with certainty: there's always some chance of error.


Question 5: A chi-square goodness-of-fit test is used to determine whether:

  1. Two quantitative variables are linearly related
  2. A single categorical variable's observed distribution matches a hypothesized (expected) distribution
  3. The means of two independent groups are significantly different
  4. A sample proportion is significantly different from a hypothesized value using a z-test

Correct Answer: B. A single categorical variable's observed distribution matches a hypothesized (expected) distribution

Explanation: A chi-square goodness-of-fit test compares the observed counts in each category of a single categorical variable to the counts you'd expect under some hypothesized distribution: for example, testing whether a die is fair by comparing observed roll counts to the expected 1/6 probability for each face. It's distinct from a chi-square test of independence, which examines the relationship between two categorical variables instead of comparing one variable to a hypothesized distribution.


More AP Statistics Study Resources

Looking for a study guide to fill a couple gaps, or just want a full length practice exam? A few resources worth checking out below. If you do find these recommendations useful, please shop through the affiliate links to help support this site.

Barron's AP Statistics Premium Study Guide

Covers all nine units with a strong emphasis on writing full-sentence, in-context conclusions, exactly what free-response graders are looking for.


Princeton Review Cracking the AP Statistics Exam

Especially useful for the Investigative Task, since it walks through how to approach an unfamiliar problem using the same reasoning framework as familiar ones.


AP Statistics Formula and Reference Sheet Practice

Practicing with the same formula sheet you'll receive on test day builds speed and familiarity before the actual exam.


Plenty of other resources exist – just do a quick internet search – but these are a good place to start.