A histogram of household incomes in a large city is strongly skewed to the right. Which statement is correct?
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About this test
This is a free 15-question sampler in the style of the AP Statistics multiple-choice section, written by the StudyPDF team for the course as revised for 2026-27. It covers all five units, from one-variable data and study design through probability, inference for proportions and means, and regression, and it mixes multiple choice, select all that apply and fill in the blank. Answer all 15, then check your score and read the worked explanation for every question.
All 15 questions at a glance
Prefer to read before you play? Every question in the sampler is listed below. Answers and explanations stay collapsed until you open them.
1.A histogram of household incomes in a large city is strongly skewed to the right. Which statement is correct?
- A. The mean is larger than the median, and the median is the better summary of a typical household
- B. The mean is smaller than the median, and the median is the better summary of a typical household
- C. The mean equals the median, so either one summarizes the center equally well
- D. The mean is larger than the median, and the mean is the better summary because it uses every value
Answer: A. The mean is larger than the median, and the median is the better summary of a typical household
In a right-skewed distribution the long tail of high values pulls the mean up toward the tail, while the median stays near the bulk of the data. So the mean is larger than the median. Because the mean is sensitive to those extreme values, the median describes a typical household better. Using every value is a weakness here, not a strength. The mean and median are about equal only for roughly symmetric distributions.
2.In the data set 3, 5, 6, 8, 9, 11, 12, the largest value is changed from 12 to 60. Which statistics stay the same?
Select all that apply.
- A. The median
- B. The interquartile range
- C. The standard deviation
- D. The range
- E. The mean
Answer: A. The median, B. The interquartile range
The median is the fourth value, 8, and it does not move. The first quartile is the median of 3, 5, 6, which is 5, and the third quartile is the median of the upper three values, 11 before and after the change, so the IQR is 6 both times. The mean jumps from 54/7 (about 7.7) to 102/7 (about 14.6), the range grows from 9 to 57, and the standard deviation grows a lot. Statistics built from the middle of the data are resistant to outliers, and statistics built from every value or from the extremes are not.
3.A county has 12 high schools. A researcher randomly selects 3 of the schools and surveys every student at those 3 schools. Which sampling method is this?
- A. Cluster sampling
- B. Stratified random sampling
- C. Simple random sampling
- D. Systematic sampling
Answer: A. Cluster sampling
The population is divided into natural groups (the schools), a random sample of whole groups is chosen, and every member of the chosen groups is surveyed. That is cluster sampling. In stratified sampling you would take some students from every group, which would mean visiting all 12 schools. A simple random sample would pick individual students from the whole county, and a systematic sample picks every kth name from a list.
4.A gardener wants to compare two fertilizers using 20 tomato plants. Ten of the plants are on the sunny side of a greenhouse and ten are on the shady side, and light is known to affect growth. Which design is best?
- A. Put every sunny plant on fertilizer A and every shady plant on fertilizer B
- B. Within the sunny plants and within the shady plants separately, randomly assign half to each fertilizer
- C. Let the gardener pick which fertilizer each plant gets
- D. Randomly assign fertilizers to all 20 plants and ignore the light difference
Answer: B. Within the sunny plants and within the shady plants separately, randomly assign half to each fertilizer
This is a randomized block design. Light is a known source of variation, so the plants are blocked by sun and shade, and the fertilizers are randomly assigned within each block. That way each fertilizer is tried equally in both light conditions and the effect of light is separated from the effect of fertilizer. The first option confounds fertilizer with light, the third invites bias, and the last one is valid but wastes the chance to remove the light variation.
5.Of 250 students surveyed, 40 play both a sport and an instrument, 90 play only a sport, 30 play only an instrument and 90 play neither. A student who plays an instrument is chosen at random. What is the probability that this student also plays a sport?
- A. 0.16
- B. 0.31
- C. 0.52
- D. 0.57
Answer: D. 0.57
The condition is that the student plays an instrument, so the sample space shrinks to the 40 + 30 = 70 instrument players. Of those, 40 also play a sport, so the probability is 40/70, about 0.57. The answer 0.31 is the reverse, 40/130, the chance that a sport player also plays an instrument. The answer 0.16 is 40/250, the chance of doing both, and 0.52 is 130/250, the chance of playing a sport at all.
6.Events A and B satisfy P(A) = 0.4, P(B) = 0.5 and P(A and B) = 0.2. Which statements are true?
Select all that apply.
- A. A and B are independent
- B. A and B are mutually exclusive
- C. P(A or B) = 0.7
- D. P(A given B) = 0.4
- E. P(A or B) = 0.9
Answer: A. A and B are independent, C. P(A or B) = 0.7, D. P(A given B) = 0.4
Independence means P(A and B) = P(A) times P(B), and 0.4 times 0.5 is 0.2, so A and B are independent. Equivalently, P(A given B) = 0.2/0.5 = 0.4, which equals P(A). For the union, P(A or B) = 0.4 + 0.5 - 0.2 = 0.7. Mutually exclusive events cannot happen together, so P(A and B) would be 0, but here it is 0.2. The value 0.9 forgets to subtract the overlap, which is counted twice.
7.Complete the sentence.
A basketball player makes 70 percent of free throws, and attempts are independent. The number of made shots in 10 attempts follows a binomial distribution with mean _____ and standard deviation about _____.
Options for blank 1: 3, 7, 7.7, 10
Options for blank 2: 2.1, 1.45, 2.65, 7
Answer: 7, 1.45
For a binomial random variable the mean is n times p = 10 times 0.7 = 7. The standard deviation is the square root of n times p times (1 - p) = sqrt(10 times 0.7 times 0.3) = sqrt(2.1), about 1.45. The value 2.1 is the variance, not the standard deviation, and 2.65 is sqrt(np), which forgets the (1 - p) factor.
8.In a random sample of 400 residents of a city, 220 support a new bus line. A 95% confidence interval for the proportion of all residents who support it is 0.501 to 0.599. Which interpretation is correct?
- A. We are 95% confident that the proportion of all residents who support the bus line is between 0.501 and 0.599
- B. 95% of the residents in the city support the bus line
- C. There is a 95% probability that a new sample proportion will fall between 0.501 and 0.599
- D. 95% of all possible samples have a sample proportion between 0.501 and 0.599
Answer: A. We are 95% confident that the proportion of all residents who support the bus line is between 0.501 and 0.599
A confidence interval is a statement about the population parameter, here the proportion of all residents. The 95% describes the method: if you repeated the sampling many times, about 95% of the intervals built this way would capture the true proportion. The interval says nothing about what percent of residents hold a view, and it is not a range for future sample proportions. Those would vary around the true value, not around this one sample's 0.55.
9.Complete the sentence.
In a random sample of 250 students, 90 own a bicycle. The sample proportion is _____, and the standard error of the sample proportion is about _____.
Options for blank 1: 0.64, 0.36, 0.28, 90
Options for blank 2: 0.48, 0.0009, 0.0304, 0.0608
Answer: 0.36, 0.0304
The sample proportion is p-hat = 90/250 = 0.36. The standard error is sqrt(p-hat times (1 - p-hat) / n) = sqrt(0.36 times 0.64 / 250) = sqrt(0.0009216), about 0.0304. The value 0.48 comes from forgetting to divide by n, 0.0009 is the variance, and 0.0608 is twice the standard error, roughly the margin of error for 95% confidence.
10.A researcher takes a separate random sample of 100 students from each of three schools and asks each student to choose a favorite lunch from four options. The goal is to decide whether the distribution of favorite lunch is the same at all three schools. Which test is appropriate, and what are its degrees of freedom?
- A. Chi-square test for independence, df = 6
- B. Chi-square test for homogeneity, df = 12
- C. Chi-square test for homogeneity, df = 6
- D. Chi-square test for independence, df = 11
Answer: C. Chi-square test for homogeneity, df = 6
Separate random samples were taken from each of several populations (the three schools) and one categorical variable was recorded, and the question is whether the distributions match. That is a test for homogeneity. Independence would apply to one random sample from one population with two categorical variables recorded. The table has 3 rows and 4 columns, so df = (3 - 1)(4 - 1) = 6. The number 12 is the count of cells, and 11 is one less than that.
11.A population has mean 50 and standard deviation 12. For random samples of size 36, what are the mean and standard deviation of the sampling distribution of the sample mean?
- A. Mean 50, standard deviation 12
- B. Mean 50, standard deviation 2
- C. Mean 50, standard deviation 0.33
- D. Mean 8.33, standard deviation 2
Answer: B. Mean 50, standard deviation 2
The sampling distribution of x-bar is centered at the population mean, 50, because the sample mean is an unbiased estimator. Its standard deviation is the population standard deviation divided by the square root of the sample size: 12/sqrt(36) = 12/6 = 2. The answer 0.33 divides by n instead of the square root of n. With n = 36 the shape is also close to normal even if the population is not, by the central limit theorem.
12.A 95% confidence interval for the difference in population means, mu_A - mu_B, based on two independent random samples, is (-1.2, 4.6). Which statements are justified?
Select all that apply.
- A. Zero is a plausible value for the difference in population means
- B. A two-sided test of H0: mu_A = mu_B at the 5% significance level would not reject H0
- C. There is a 95% probability that the difference in sample means is between -1.2 and 4.6
- D. The data prove that the two population means are equal
- E. The interval shows mean A is larger than mean B
Answer: A. Zero is a plausible value for the difference in population means, B. A two-sided test of H0: mu_A = mu_B at the 5% significance level would not reject H0
Because 0 lies inside the interval, a difference of 0 is a plausible value, and a two-sided test at the matching 5% level would not reject the null hypothesis of no difference. That is not the same as proving the means are equal. The data are simply not convincing evidence of a difference. The sample difference is the center of the interval and is known, so there is no probability statement to make about it. And since the interval includes negative values, it does not show that mean A is the larger one.
13.A least-squares line for predicting exam score from hours studied is: predicted score = 52 + 6.5(hours). Which is the correct interpretation of the slope?
- A. A student who studies 0 hours is predicted to score 6.5
- B. Every student who studies one more hour scores exactly 6.5 points higher
- C. 6.5 percent of the variation in exam scores is explained by hours studied
- D. For each additional hour studied, the predicted exam score increases by about 6.5 points
Answer: D. For each additional hour studied, the predicted exam score increases by about 6.5 points
The slope is the change in the predicted response for each one-unit increase in the explanatory variable, so each extra hour goes with about 6.5 more points on average. It describes the model's prediction, not a guarantee for each student, which rules out the second option. The intercept, 52, is the predicted score at 0 hours. The percent of variation explained is r squared, a different quantity.
14.Complete the sentence.
A linear model has a correlation of r = -0.80. About _____ percent of the variation in the response is explained by its linear relationship with the explanatory variable, and the slope of the least-squares line is _____.
Options for blank 1: 8, 64, 80, 20
Options for blank 2: positive, zero, negative, equal to -0.80
Answer: 64, negative
The proportion of variation explained is r squared: (-0.80) squared is 0.64, so about 64 percent. The slope always has the same sign as r, so a negative correlation means a negative slope. The slope is not equal to r in general, because it also depends on the ratio of the two standard deviations: slope = r times (s_y / s_x).
15.A least-squares line for predicting weight in kilograms from height in centimeters is: predicted weight = -12 + 0.5(height). A person who is 170 cm tall weighs 68 kg. What is the residual?
- A. 73 kg
- B. 5 kg
- C. -5 kg
- D. 68 kg
Answer: C. -5 kg
The predicted weight is -12 + 0.5(170) = 73 kg. A residual is the actual value minus the predicted value, so it is 68 - 73 = -5 kg. The negative sign means the line overestimates this person's weight. The value 73 is the prediction itself, and 5 kg has the sign reversed.
What the revised AP Statistics exam looks like and how it is weighted
The AP Statistics exam is scored 1 to 5 and was revised for the 2026-27 school year, so the first exam in the new format is the May 2027 one. According to the College Board, Section I is 42 multiple-choice questions in 1 hour 30 minutes and Section II is 4 free-response questions in 1 hour 30 minutes, and each section is worth 50 percent of the score. Each multiple-choice question now has 4 answer choices instead of 5, two sets of 3 questions share one prompt (one on probability and distributions, one on regression), and each free-response question is worth 10 points. The exam is fully digital in the Bluebook app, free-response answers included, and calculators are permitted. Practice tests and review books written before the revision describe 40 questions with 5 choices and 6 free-response questions, so check the year on anything you find.
The course is now five units instead of nine, and the College Board publishes how much of the exam score each one gets. Exploring one-variable data and collecting data is 20 to 30 percent, probability, random variables and probability distributions 15 to 25, inference for categorical data (proportions) 15 to 25, inference for quantitative data (means) 10 to 20, and regression analysis 10 to 20. The revision also dropped a few topics: the chi-square goodness-of-fit test, the geometric distribution, combining random variables and the whole unit on inference for slopes. The chi-square test for homogeneity or independence stays. If your practice material still has a slope-inference or goodness-of-fit problem, it is from the old course.
A 5 is the top score, but what a score is worth is up to each college. Some give credit for a 3, many ask for a 4 or a 5, and policies differ by school. Look up the colleges you care about before you decide how hard to push.
How to use this sampler, and how to take it on paper
The 15 questions are spread across the five units, with four on the heaviest one, one-variable data and study design, and two on inference for means. They ask for the reasoning behind a result more than the arithmetic: why the median is the better summary of a skewed distribution, why blocking beats a completely randomized design when a known factor matters, what a 95 percent confidence level actually claims, why a confidence interval that contains 0 does not prove two means are equal. That is also the thinking the free-response questions score.
Take it in one sitting with scratch paper, and use a calculator for the few square roots, as you would on the real exam. Then read the explanation for every question, including the ones you got right. Treat a miss as a topic. If you missed the confidence interval question and the standard error question, the gap is probably what a sampling distribution is, not two separate formulas. Math is written in plain text here, so p-hat means the sample proportion and x-bar means the sample mean.
If you would rather work on paper, use the Download test as PDF button above the questions. The file has all 15 questions with an answer key on the last page and needs a free StudyPDF account. The questions are original and written to the published course outline. They are not released exam questions, and this sampler does not practice the free-response section. For that, work through the College Board's released free-response questions, keeping in mind that earlier years use the old six-question format. On a free-response question the points come from naming the procedure, checking the conditions, doing the calculation and concluding in context.
How StudyPDF builds AP Statistics practice tests from your class notes
Fifteen questions can show you which unit is shaky. They cannot get you ready on their own, and a generic bank rarely matches the datasets, notation and examples your teacher actually uses.
StudyPDF works from your material instead. Upload your textbook chapters, your teacher's slides, a worked problem set or your review packet, press New material, and StudyPDF builds practice tests from those exact pages. Every question is grounded in your material and every explanation cites where the answer comes from, so you can go straight back to the page when a step does not make sense.
You do not need to upload anything to start. Name a topic instead, for example confidence intervals for a proportion or the chi-square test, and Bo sets it up with its key concepts so you can build quizzes and flashcards on it. Your results track which concepts you keep missing, so the next practice test can target them. Starting is free.
Written by the StudyPDF team. Last updated August 19, 2026.
Good to know
Is this AP Statistics practice test free?
Yes. All 15 questions, the score screen and every worked explanation are free, and the quiz runs in your browser. A free StudyPDF account is needed to download the test as a PDF with an answer key or to build more practice tests from your own notes.
Who wrote these questions?
The StudyPDF team wrote every question and explanation, following the five units of the published AP Statistics course outline for 2026-27. They are original items, not real or released exam questions, and StudyPDF is not affiliated with the College Board, which does not endorse this page.
Does this match the revised 2026-27 course?
Yes. It uses the five-unit structure and leaves out the topics the College Board removed, including inference for slopes and the chi-square goodness-of-fit test. The real multiple-choice section now has 4 choices per question and one correct answer. This sampler also uses select all that apply and fill in the blank, because judging each option separately is a good check of a unit. It does not practice the four free-response questions.
Can I get practice tests built from my own class materials?
Yes. Upload your textbook chapters, slides, problem sets or review packet to StudyPDF and you can build practice tests from those exact pages, with explanations tied to your sources. If you have nothing to upload, name a topic or a unit instead.