AP Statistics Practice Test — 20 Free Questions with Explanations (2026)

Free AP Statistics practice test with 20 multiple-choice questions covering all major exam topics. Every question includes the correct answer and a full explanation. Use this to find gaps before test day.

AP Statistics Exam Format (2026)

The investigative task (the last FRQ) is worth more than the other FRQs and often requires connecting multiple statistical concepts.

AP Statistics Practice Test: 20 Questions

Exploring Data

Question 1. A dataset has a mean of 50 and a median of 35. Which of the following best describes the distribution?

A) Symmetric
B) Skewed left (negatively skewed)
C) Skewed right (positively skewed)
D) Bimodal

Answer: C

When the mean is greater than the median, the distribution is skewed right (positively skewed). High outliers or a long right tail pull the mean up, while the median remains resistant to extreme values. Skewed left would have mean less than median.

Question 2. A boxplot shows the following five-number summary: Min = 10, Q1 = 25, Median = 40, Q3 = 60, Max = 110. Which value is an outlier using the 1.5 × IQR rule?

A) 10
B) 40
C) 110
D) There are no outliers

Answer: C

IQR = Q3 - Q1 = 60 - 25 = 35. Upper fence = Q3 + 1.5(35) = 60 + 52.5 = 112.5. Lower fence = Q1 - 1.5(35) = 25 - 52.5 = -27.5. Max = 110 is within the fences, so technically there are no outliers. Wait — 110 < 112.5, so no outliers. If the max were 115, it would be an outlier. The answer here is D — no outliers, since 110 < 112.5.

Correction — Answer: D

110 is less than 112.5 (the upper fence), so it is not an outlier. This question tests careful application of the rule rather than visual assumption.

Question 3. Two variables have a correlation coefficient of r = -0.82. Which statement is most accurate?

A) An increase in the explanatory variable causes a decrease in the response variable
B) There is a strong positive linear relationship
C) There is a strong negative linear relationship
D) About 82% of the variation in Y is explained by X

Answer: C

r = -0.82 indicates a strong (close to -1) negative linear relationship. Option A incorrectly implies causation — correlation does not establish cause. Option D describes r-squared (coefficient of determination): r² = 0.67, meaning 67% of variance in Y is explained by X.

Sampling and Experimentation

Question 4. A school wants to survey student opinions on a new dress code. They randomly select 3 homeroom classes and survey every student in those classes. This is an example of:

A) Simple random sampling
B) Stratified random sampling
C) Cluster sampling
D) Systematic sampling

Answer: C

Cluster sampling divides the population into groups (clusters) and randomly selects entire clusters to study. Here, each homeroom class is a cluster. Stratified sampling would randomly select individuals from each homeroom. Simple random sampling would select individual students randomly from the entire school.

Question 5. A researcher randomly assigns 60 patients to receive either a new drug or a placebo, then measures recovery time. Neither the patients nor the doctors measuring recovery know which treatment was given. This is best described as:

A) An observational study with random assignment
B) A double-blind randomized experiment
C) A matched pairs design
D) A single-blind experiment with blocking

Answer: B

This is a double-blind randomized experiment: random assignment controls for confounding variables, and neither patients nor researchers know the treatment condition, preventing expectation effects. A matched pairs design would pair similar subjects and assign them to different treatments.

Question 6. A polling company surveys 1,000 people by calling landline phone numbers selected randomly. A concern about this study is:

A) The sample size is too small to draw any conclusions
B) Voluntary response bias from people choosing to answer
C) Undercoverage bias because people without landlines are excluded
D) Measurement bias from question wording

Answer: C

Undercoverage bias occurs when some members of the population cannot be selected. People who only use cell phones, younger adults, and lower-income households are underrepresented in a landline-only sample, potentially skewing results. The sample size of 1,000 is adequate for many national polls.

Probability

Question 7. A bag contains 4 red and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that both marbles are red?

A) 4/10 × 4/10 = 16/100
B) 4/10 × 3/9 = 12/90
C) 4/10 × 3/10 = 12/100
D) 6/10 × 4/9 = 24/90

Answer: B

Without replacement, drawing changes the composition of the bag. P(first red) = 4/10. Given first was red, P(second red) = 3/9. P(both red) = (4/10)(3/9) = 12/90 = 2/15 ≈ 0.133. Option A incorrectly uses independent probabilities (with replacement).

Question 8. A random variable X has the following distribution: P(X = 1) = 0.2, P(X = 2) = 0.3, P(X = 3) = 0.5. What is the expected value E(X)?

A) 2.0
B) 2.3
C) 2.5
D) 3.0

Answer: B

E(X) = 1(0.2) + 2(0.3) + 3(0.5) = 0.2 + 0.6 + 1.5 = 2.3. Expected value is the probability-weighted average of all possible outcomes.

Random Variables and Probability Distributions

Question 9. A basketball player makes free throws with probability 0.75 independently on each shot. If she shoots 8 free throws, what is the probability that she makes exactly 6? (Use binomial formula.)

A) C(8,6)(0.75)^6(0.25)^2
B) C(8,6)(0.25)^6(0.75)^2
C) (0.75)^6
D) 6/8

Answer: A

This is a binomial setting: fixed number of trials (n=8), two outcomes, constant probability (p=0.75), independent trials. P(X = 6) = C(8,6)(0.75)^6(0.25)^2. C(8,6) = 28, so P = 28(0.75)^6(0.25)^2 ≈ 0.311.

Question 10. The heights of adult men in a population are normally distributed with mean 70 inches and standard deviation 3 inches. What is the z-score for a man who is 76 inches tall?

A) 1.5
B) 2.0
C) 2.5
D) 3.0

Answer: B

z = (x - mean) / SD = (76 - 70) / 3 = 6/3 = 2.0. A z-score of 2 means the man is 2 standard deviations above the mean. Using the empirical rule, about 2.5% of men are taller than 76 inches.

Sampling Distributions

Question 11. A random sample of size n = 100 is drawn from a population with mean 50 and standard deviation 20. What is the standard deviation of the sampling distribution of the sample mean (standard error)?

A) 20
B) 2
C) 0.2
D) 200

Answer: B

Standard error of the mean = SD / sqrt(n) = 20 / sqrt(100) = 20/10 = 2. As sample size increases, the sampling distribution becomes narrower (more precise estimates). This is the central limit theorem in action.

Question 12. Which condition must be checked to use the normal approximation for a sampling distribution of a sample proportion?

A) np ≥ 10 and n(1-p) ≥ 10
B) n ≥ 30
C) The population must be normally distributed
D) The sample must be stratified

Answer: A

For the sampling distribution of a sample proportion to be approximately normal, both np and n(1-p) must be at least 10 (the Large Counts condition). This ensures there are enough expected successes and failures. The n ≥ 30 rule applies to the sampling distribution of a sample mean, not proportion.

Inference: Confidence Intervals

Question 13. A 95% confidence interval for the mean weight of a bag of chips is (14.8 oz, 15.4 oz). Which interpretation is correct?

A) 95% of all chip bags weigh between 14.8 and 15.4 oz
B) There is a 95% probability that the true mean is between 14.8 and 15.4 oz
C) If this procedure were repeated many times, about 95% of intervals constructed this way would contain the true mean
D) The true mean is definitely between 14.8 and 15.4 oz

Answer: C

The correct frequentist interpretation: the 95% refers to the procedure, not this specific interval. Once calculated, the true mean is either in this interval or it is not — we just do not know which. About 95% of intervals constructed using this method from repeated samples would contain the true mean.

Question 14. All else being equal, which change would produce a narrower confidence interval?

A) Increasing confidence level from 90% to 99%
B) Decreasing sample size from 200 to 50
C) Increasing sample size from 50 to 200
D) Increasing population standard deviation

Answer: C

Margin of error = z* × (SD / sqrt(n)). Increasing sample size increases sqrt(n) in the denominator, reducing margin of error and producing a narrower interval. Higher confidence level requires a larger z*, widening the interval. Higher SD widens the interval.

Inference: Significance Tests

Question 15. A two-tailed t-test produces a p-value of 0.03. At the significance level alpha = 0.05, the correct conclusion is:

A) Fail to reject H0; the result is not statistically significant
B) Reject H0; there is statistically significant evidence against the null
C) Accept H0; the null hypothesis is true
D) Reject Ha; the alternative hypothesis is false

Answer: B

Since p-value (0.03) < alpha (0.05), we reject the null hypothesis. The result is statistically significant at the 0.05 level. We never "accept" H0 — we only "fail to reject" it. Rejecting H0 does not prove Ha is true, but it provides significant evidence against H0.

Question 16. A Type I error in hypothesis testing occurs when:

A) You fail to reject a false null hypothesis
B) You reject a true null hypothesis
C) The sample size is too small to detect an effect
D) The p-value is less than alpha by chance

Answer: B

A Type I error is a false positive: rejecting H0 when it is actually true. The probability of a Type I error equals the significance level alpha. A Type II error (option A) is a false negative: failing to reject a false null hypothesis. The probability of a Type II error is beta; power = 1 - beta.

Question 17. A chi-square test for association is performed on a 2×2 contingency table. Which is a required condition for this test?

A) The data must come from a normal distribution
B) All expected cell counts must be at least 5
C) The two variables must have equal proportions
D) Sample size must exceed 100

Answer: B

The chi-square test requires that all expected cell counts be at least 5 (the large counts condition). If this fails, the chi-square approximation is unreliable and you may need to use Fisher's exact test. The data are categorical, so normality does not apply.

Inference for Regression

Question 18. A regression analysis of height (x) and weight (y) produces the equation: predicted weight = -100 + 3.5(height), where height is in inches and weight in pounds. What is the interpretation of the slope?

A) For each additional inch of height, weight increases by 100 pounds
B) The average weight when height = 0 is -100 pounds
C) For each additional inch of height, weight is predicted to increase by 3.5 pounds
D) 3.5% of the variation in weight is explained by height

Answer: C

The slope (3.5) represents the predicted change in the response variable (weight) for each one-unit increase in the explanatory variable (height). The y-intercept (-100) represents predicted weight at height = 0, which is not meaningful here (no person has 0-inch height).

Question 19. A significance test for the slope in a linear regression yields t = 4.12 with p-value = 0.001. What can you conclude?

A) There is strong evidence of a linear relationship between x and y in the population
B) The slope is equal to zero in the population
C) The correlation coefficient r = 4.12
D) 41.2% of variation in y is explained by x

Answer: A

The t-test for slope tests H0: beta = 0 (no linear relationship) vs Ha: beta ≠ 0. A small p-value (0.001 << 0.05) provides strong evidence to reject H0, concluding there is a statistically significant linear relationship between x and y in the population. The t-statistic is not the same as r.

Question 20. A researcher conducts a two-sample t-test comparing mean test scores between two teaching methods. The p-value is 0.18. Which conclusion is most appropriate?

A) Method A is better than Method B
B) The two methods produce the same results
C) There is insufficient evidence to conclude the means differ
D) The null hypothesis has been proven true

Answer: C

When p > alpha (assuming alpha = 0.05), we fail to reject H0. This means we do not have sufficient evidence to conclude the population means are different — it does not mean we have proven they are equal. We never prove H0; we only fail to find evidence against it. Option B implies proof of equivalence, which is incorrect.

Score Estimation

Use our AP Statistics Score Calculator to estimate your full exam score.

AP Statistics Score Cutoffs (2026)

What AP Statistics Topics Are Most Tested

Inference dominates the exam — if you can set up, execute, and interpret confidence intervals and significance tests for means, proportions, chi-square, and regression, you are prepared for the bulk of the exam.

AP Statistics FRQ Tips

• Show all work — partial credit is available even with a wrong final answer
• State hypotheses in words — define parameters using symbols AND plain language
• Check conditions — always verify random, normal/large counts, and independence conditions before running a test
• Interpret in context — never give a generic answer; connect everything to the specific scenario in the problem
• Investigative task — read carefully, it usually has 4–6 parts that build on each other; do not skip early parts

Related Resources

• AP Statistics Score Calculator
• Is AP Stats Hard?
• AP Score Distributions 2026
• How to Score a 5 on Any AP Exam
• See all AP calculators