AP Statistics, AP exams

Unit 1: Exploring One-Variable Data and Collecting Data

Unit 1 combines descriptive statistics with study design, which in the revised framework are taught together as the front half of the investigative process. Students describe distributions of categorical and quantitative data, then learn how sampling method and experimental design determine what conclusions the data can support. The distinction between an observational study and an experiment governs a large share of exam questions.

Position: 1 of 5 units
Topics covered: 6 topics in this guide

What is covered

Topics inside this unit.

These topics describe the scope students most often review for this part of AP Statistics. Treat them as a study checklist rather than an exhaustive list of what a single exam form can sample.

Investigative questions: Framing a statistical question that data can actually answer, and identifying the variables involved.
Displays of categorical and quantitative data: Bar charts, two-way tables, dotplots, histograms, and boxplots, and choosing the right display.
Describing distributions: Shape, center, variability, and outliers, described in context rather than as isolated numbers.
Standardized scores and the normal model: Using z-scores to compare values from different distributions and to work with normal distributions.
Sampling methods and bias: Simple random, stratified, cluster, and systematic sampling, and the biases each is meant to reduce.
Experimental design: Treatments, control, random assignment, replication, blocking, and what each permits you to conclude.

Study tips

How to practice Data and Collection.

Section-specific guidance that follows from how this material is usually tested.

Describe every distribution with shape, center, variability, and unusual features, in context, every single time.
Practice stating explicitly whether random sampling or random assignment was used, since one licenses generalization and the other licenses causal claims.
Write comparisons using explicit comparative language; the rubric requires an actual comparison, not two separate descriptions.

Where this fits

Unit 1: Exploring One-Variable Data and Collecting Data is 1 of 5 units in the AP Statistics guide. Use the full guide to balance it against everything else you have to review.

Back to the AP Statistics guide Official exam information

Sample Data and Collection questions

Practice questions, not yet expert-reviewed

Original practice questions written to the published framework for this section. No expert has reviewed them, and they are not taken from any official exam. Try each one before you open the answer.

Question 1Foundational
Test scores are approximately normally distributed with mean 70 and standard deviation 8. What is the standardized score (z-score) of a score of 86?
1. A2
2. B1.6
3. C-2
4. D16
Show answer
Answer: A. 2
A z-score is (value - mean)/standard deviation = (86 - 70)/8 = 16/8 = 2, so the score sits two standard deviations above the mean. Answering 16 stops at the deviation without dividing, and 1.6 divides by 10 rather than by the given standard deviation.
Key insight: A z-score counts standard deviations from the mean, which is what makes different distributions comparable.
Question 2Foundational
Volunteers for a study are randomly assigned to take either a new supplement or a placebo, and a statistically significant difference in outcomes is found. What conclusion does the random assignment support?
1. AThat the supplement caused the difference, for the volunteers in the study
2. BThat the results generalize to all adults
3. CBoth causation and generalization to a larger population
4. DNeither causation nor any conclusion about the volunteers
Show answer
Answer: A. That the supplement caused the difference, for the volunteers in the study
Random assignment balances confounding variables across the treatment groups, which is what licenses a cause-and-effect conclusion. Generalization to a wider population requires random selection from that population, and volunteers are not a random sample, so the causal claim stays limited to the subjects studied.
Key insight: Random assignment licenses causation; random sampling licenses generalization.
Question 3Intermediate
A data set consists of the values 4, 5, 6, 7, and 100. Which measure of center best describes a typical value in this data set?
1. AThe median
2. BThe mean
3. CThe range
4. DThe standard deviation
Show answer
Answer: A. The median
The value 100 is a strong outlier that pulls the mean up to 24.4, far above every value except itself, while the median stays at 6. The median is resistant to outliers, and the range and standard deviation measure variability rather than center.
Key insight: Use resistant measures, the median and the interquartile range, when a distribution is skewed or has outliers.
Question 4Intermediate
A school divides its students by grade level and then takes a separate random sample from within each grade. What sampling method is this?
1. AStratified random sampling
2. BCluster sampling
3. CSystematic sampling
4. DConvenience sampling
Show answer
Answer: A. Stratified random sampling
Sampling within groups that are formed to be similar internally is stratified sampling, and it reduces variability by guaranteeing representation from every grade. Cluster sampling would instead choose whole grades at random and survey everyone inside the chosen clusters.
Key insight: Stratified sampling samples within every group; cluster sampling samples whole groups.
Question 5Advanced
Scores are approximately normally distributed with mean 500 and standard deviation 100. Using the empirical rule, approximately what percent of scores fall between 400 and 700?
1. AAbout 81.5%
2. BAbout 68%
3. CAbout 95%
4. DAbout 47.5%
Show answer
Answer: A. About 81.5%
The bounds are one standard deviation below and two above the mean. The empirical rule puts about 34% between the mean and one standard deviation below, and about 47.5% between the mean and two above, for a total of about 81.5%. Answering 95% assumes a symmetric interval two standard deviations wide on both sides.
Key insight: Split an asymmetric normal interval at the mean and add the two halves separately.

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Unit 1: Exploring One-Variable Data and Collecting Data