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← AP Statistics
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Prepare for the timed AP Statistics test.

Your answers are held until submission. The final review identifies the units that need another pass.

AP Statistics coverage and review map

Connect every question to the exact skill it rehearses. Work through the units in order, then return to any topic that still needs a hint or a second attempt.

01

One-Variable Data and Collecting Data

Distributions, sampling, experiments, bias, ethical data collection

Goal: recognise a one-variable data and collecting data problem from its wording, carry out the governing method, and check that the result is reasonable.

02

Probability, Random Variables, and Distributions

Simulation, probability rules, discrete and continuous variables

Goal: recognise a probability, random variables, and distributions problem from its wording, carry out the governing method, and check that the result is reasonable.

03

Inference for Categorical Data: Proportions

Sampling distributions, intervals, and tests for proportions

Goal: recognise a inference for categorical data: proportions problem from its wording, carry out the governing method, and check that the result is reasonable.

04

Inference for Quantitative Data: Means

Intervals and tests for means and paired data

Goal: recognise a inference for quantitative data: means problem from its wording, carry out the governing method, and check that the result is reasonable.

05

Regression Analysis

Two-variable data, linear models, inference for slopes

Goal: recognise a regression analysis problem from its wording, carry out the governing method, and check that the result is reasonable.

AP Statistics questions with worked answers

These 8 questions are printed in full on this page and are drawn across all 5 course units. Nothing here is generated on the fly. Cover the options, solve each one on paper, and only then open the worked answer to compare your method with the one shown.

Question 1: A data set has Q1 = 20 and Q3 = 32. Using the 1.5 IQR rule, what is the upper fence for outliers?

AP Statistics · One-Variable Data and Collecting Data

  1. 50
  2. 44
  3. 48
  4. 38
Show the worked answer
  1. The IQR is Q3 - Q1 = 32 - 20 = 12.
  2. 1.5 times the IQR is 1.5 x 12 = 18.
  3. The upper fence is Q3 plus that amount.
  4. 32 + 18 = 50, so any value above 50 is flagged as an outlier.

Answer: 50

Question 2: Researchers split a school by grade level, then take a random sample within each grade. What sampling design is this?

AP Statistics · One-Variable Data and Collecting Data

  1. Stratified random sampling
  2. Cluster sampling
  3. Systematic sampling
  4. Convenience sampling
Show the worked answer
  1. The population is first divided into groups that share a trait, here grade level.
  2. A random sample is then drawn from inside every group.
  3. That is the definition of stratified sampling.
  4. Cluster sampling would instead pick whole grades at random and survey everyone in them.

Answer: Stratified random sampling

Question 3: X has mean 12 and standard deviation 3. What are the mean and standard deviation of Y = 2X - 5?

AP Statistics · Probability, Random Variables, and Distributions

  1. mean 19, standard deviation 6
  2. mean 19, standard deviation 1
  3. mean 24, standard deviation 6
  4. mean 19, standard deviation 6.5
Show the worked answer
  1. Means follow the whole transformation: 2(12) - 5 = 24 - 5 = 19.
  2. Adding or subtracting a constant slides the distribution but does not change its spread.
  3. Multiplying by 2 doubles the spread.
  4. So the standard deviation is 2 x 3 = 6.

Answer: mean 19, standard deviation 6

Question 4: Scores are normal with mean 65 and standard deviation 4. What proportion is below 70?

AP Statistics · Probability, Random Variables, and Distributions

  1. 0.8944
  2. 0.7734
  3. 0.1056
  4. 0.6915
Show the worked answer
  1. Convert to a z score: (70 - 65) / 4.
  2. 5 / 4 = 1.25.
  3. Look up the area to the left of z = 1.25 in a standard normal table.
  4. That area is 0.8944, so about 89% of scores fall below 70.

Answer: 0.8944

Question 5: In a sample of 200, the sample proportion is 0.6. What is the 95% confidence interval, to three decimal places?

AP Statistics · Inference for Categorical Data: Proportions

  1. (0.532, 0.668)
  2. (0.565, 0.635)
  3. (0.510, 0.690)
  4. (0.594, 0.606)
Show the worked answer
  1. The standard error is the square root of (0.6)(0.4) / 200 = the square root of 0.0012.
  2. That is about 0.03464.
  3. The 95% margin of error is 1.96 x 0.03464 = 0.0679.
  4. 0.6 - 0.0679 = 0.532 and 0.6 + 0.0679 = 0.668.

Answer: (0.532, 0.668)

Question 6: A sample of 25 has mean 52.4 and standard deviation 6, testing H0: mu = 50. What are the t statistic and degrees of freedom?

AP Statistics · Inference for Quantitative Data: Means

  1. t = 2.0 with 24 degrees of freedom
  2. t = 2.0 with 25 degrees of freedom
  3. t = 0.4 with 24 degrees of freedom
  4. t = 10.0 with 24 degrees of freedom
Show the worked answer
  1. The standard error is 6 divided by the square root of 25, which is 6 / 5 = 1.2.
  2. The difference from the claimed mean is 52.4 - 50 = 2.4.
  3. 2.4 / 1.2 = 2.0.
  4. A one-sample t test uses n - 1 = 24 degrees of freedom.

Answer: t = 2.0 with 24 degrees of freedom

Question 7: A least-squares regression reports r = 0.72. What percentage of the variation in y does the model explain?

AP Statistics · Regression Analysis

  1. 51.8%
  2. 72.0%
  3. 84.9%
  4. 28.0%
Show the worked answer
  1. The share of variation explained is r squared, not r.
  2. 0.72 x 0.72 = 0.5184.
  3. As a percentage that is 51.84%.
  4. So about 51.8% of the variation in y is explained by the linear model.

Answer: 51.8%

Question 8: A regression predicts 78.5 for a case whose actual value is 74. What is the residual?

AP Statistics · Regression Analysis

  1. -4.5
  2. 4.5
  3. 78.5
  4. -74
Show the worked answer
  1. A residual is always observed minus predicted.
  2. The observed value is 74 and the prediction is 78.5.
  3. 74 - 78.5 = -4.5.
  4. The negative residual means the point sits below the regression line.

Answer: -4.5

Which unit each printed question belongs to

Use this map after marking your work. If two misses share a unit, review that unit before starting a generated set.

The 8 printed AP Statistics questions, the unit each one tests, and its answer.
QuestionUnitWhat it asksAnswer
1One-Variable Data and Collecting DataA data set has Q1 = 20 and Q3 = 32. Using the 1.5 IQR rule, what is the upper fence for outliers?50
2One-Variable Data and Collecting DataResearchers split a school by grade level, then take a random sample within each grade. What sampling design is this?Stratified random sampling
3Probability, Random Variables, and DistributionsX has mean 12 and standard deviation 3. What are the mean and standard deviation of Y = 2X - 5?mean 19, standard deviation 6
4Probability, Random Variables, and DistributionsScores are normal with mean 65 and standard deviation 4. What proportion is below 70?0.8944
5Inference for Categorical Data: ProportionsIn a sample of 200, the sample proportion is 0.6. What is the 95% confidence interval, to three decimal places?(0.532, 0.668)
6Inference for Quantitative Data: MeansA sample of 25 has mean 52.4 and standard deviation 6, testing H0: mu = 50. What are the t statistic and degrees of freedom?t = 2.0 with 24 degrees of freedom
7Regression AnalysisA least-squares regression reports r = 0.72. What percentage of the variation in y does the model explain?51.8%
8Regression AnalysisA regression predicts 78.5 for a case whose actual value is 74. What is the residual?-4.5

How the generated AP Statistics sets are created

The 8 questions above are fixed and checked. The generator at the top of the page is different: it writes fresh questions with AI from the course and unit information shown here, then the application checks each one for a complete prompt, four choices, one keyed answer, and an explanation. Generated questions are original practice—not official or released exam questions—and AI can still make mathematical mistakes. Verify a disputed answer with the stated method, your course materials, or the MathGPT solver, and follow the site's academic-integrity guidance.

Questions about this AP Statistics course test

What does this page cover?

It covers all 5 AP Statistics units listed above.

When can I see correct answers and explanations?

Submit the full test first. The result screen then shows every response, the correct answer, and the explanation so you can review each miss.

How long is each section of the AP Statistics exam?

Multiple choice: 1 hour 30 minutes, 42 questions. Free response: 1 hour 30 minutes, 4 questions.

Which AP Statistics sections allow a graphing calculator?

Rules change from section to section. Multiple choice: graphing calculator with statistics functions. Free response: graphing calculator with statistics functions. Provided for the whole exam: formula sheet and tables. Practise each section under its own rule.

Which AP Statistics units does this test cover?

All five: One-Variable Data and Collecting Data, Probability, Random Variables, and Distributions, Inference for Categorical Data: Proportions, Inference for Quantitative Data: Means, Regression Analysis. Study first: One-Variable Data and Collecting Data (20–30%) carries the largest published weighting.

What should I check first when I review a missed AP Statistics question?

Conditions are graded separately from the computation. A perfect p-value with no condition check scores well below a rough p-value with the conditions verified.

What should I do with a missed question?

Classify the miss as a definition, setup, calculation, interpretation, or timing error. Re-solve it from a blank page, then use the MathGPT tutor for a hint or method check.