AP Statistics Unit 1 review: Exploring One-Variable Data and Collecting Data
Unit 1 describes one-variable data and explains how samples and experiments produce evidence. In the revised 2026–27 course it is 20–30% of multiple choice. Expect calculations of center and spread, comparisons in context, and decisions about bias, causation and generalization.
Unit 1 on the May 2027 exam
| 2027 exam | |
|---|---|
| Weight | 20–30% of the multiple-choice section |
| Exam date | Tuesday, May 11, 2027, afternoon session |
| Multiple choice | 42 questions in 90 minutes, worth 50% of the exam score |
| Free response | 4 questions in 90 minutes, worth 50%. All answers are entered in Bluebook: two multi-focus questions, one inference question and a final multi-focus question. |
| Calculator | A graphing calculator with statistical capabilities is expected on both sections. Bluebook includes Desmos graphing. Nongraphing handheld calculators are not allowed in 2027. |
| Class time | About 26 class periods in College Board's pacing guide |
| 2026 results | 17% of students scored a 5 on the whole exam, and about 62% scored 3 or higher |
Sources: College Board's course and exam description, exam page, 2027 exam dates and score distributions.
What Unit 1 covers
College Board's course description splits the unit into 13 topics. The second column is what you should be able to do for each one.
| Topic | What you should be able to do |
|---|---|
| 1.1 Introducing Statistics: What Can We Learn from Data? | Formulate an investigative question that anticipates variability and identifies a population and variable. |
| 1.2 Variables | Identify observational units and distinguish categorical from quantitative variables. |
| 1.3 Tabular Representation and Summary Statistics for One Categorical Variable | Construct frequency tables and calculate counts, proportions and percentages for a category. |
| 1.4 Graphical Representations for One Categorical Variable | Choose and interpret bar or other appropriate categorical displays. |
| 1.5 Graphical Representations for One Quantitative Variable | Construct and interpret quantitative displays such as dotplots, histograms and stemplots. |
| 1.6 Descriptions for One Quantitative Variable Distributions | Describe shape, center, variability and unusual features in context. |
| 1.7 Summary Statistics for One Quantitative Variable | Calculate and interpret mean, median, standard deviation and other summaries. |
| 1.8 Graphical Representations of Summary Statistics for One Quantitative Variable | Use boxplots and the five-number summary to represent center and spread. |
| 1.9 Comparisons of the Distributions for One Quantitative Variable | Compare distributions directly using their centers, variability, shapes and unusual features. |
| 1.10 The Investigative Question Revisited and Data Collection | Choose data-collection methods that address an investigative question and its population. |
| 1.11 Random Sampling | Distinguish simple random, stratified, cluster and other random sampling methods. |
| 1.12 Potential Problems with Sampling | Explain undercoverage, nonresponse and response bias and their likely effects. |
| 1.13 Experimental Design | Design randomized experiments with comparison, control, replication and appropriate blocking. |
What a study design lets you conclude
Random selection and random assignment solve different problems. The conclusion must match how the data were obtained.
| Design feature | What it supports | What it does not establish alone |
|---|---|---|
| Random sample from a defined population | Generalization to that population, subject to sampling uncertainty | A causal effect of an observed exposure. |
| Random assignment to treatments | A causal comparison when a treatment effect is supported | Representativeness of volunteers for a broader population. |
| Both selection and assignment | Population generalization and a causal comparison | Perfect balance or certainty from one sample. |
| Blocking before random assignment | Treatment comparisons among units similar on a relevant variable | Removal of all uncontrolled differences. |
| Large convenience sample | A detailed description of the people who participated | Correction of systematic selection bias. |
| Median and IQR | Resistant summaries for skewed data or outliers | A full description of shape or unusual features. |
| Mean and standard deviation | Numerical center and spread using every observation | Resistance to extreme observations. |
Common mistakes
Each of these loses points on questions you otherwise understand.
- Listing an acronym without describing the actual distribution. Include context, units, center, spread, shape and unusual features. CED printed pp. 25–26.
- Using random selection to justify causation or random assignment to justify representativeness. These support different conclusions. CED p. 26.
- Naming bias without explaining a mechanism. State who is missed or less likely to respond and how that could affect the estimate when the context supports a direction. CED pp. 25–26.
- Claiming a large sample removes selection bias. More observations reduce sampling variability, not a systematic sampling defect. CED topic 1.12.
6 practice questions with answers
Written by Ashore for this page, in the style of the multiple-choice section. Try each one before you open the answer.
Question 1 · 1.7
Five delivery times are 12, 14, 14, 16 and 24 minutes. What are the mean and median?
- AMean 14, median 16
- BMean 16, median 14
- CMean 16, median 16
- DMean 14, median 14
Show the answer
B. The total is 80 minutes, so the mean is 80/5 = 16. The middle ordered value is 14. The longer delivery pulls the mean above the median.
Question 2 · 1.8
A distribution has Q1 = 18 and Q3 = 30. Using the 1.5 × IQR rule, which value is a high outlier?
- A42
- B46
- C48
- D49
Show the answer
D. IQR = 30 − 18 = 12. The upper fence is 30 + 1.5(12) = 48. A value must exceed the fence, so 49 is a high outlier; 48 is on the fence.
Question 3 · 1.7
A data set has mean 10 and standard deviation 2. Every value is transformed by y = 3x + 5. What are the new mean and standard deviation?
- AMean 35, SD 6
- BMean 30, SD 6
- CMean 35, SD 11
- DMean 15, SD 2
Show the answer
A. The mean becomes 3(10) + 5 = 35. Multiplication scales standard deviation by |3| to 6; adding 5 shifts all values equally and does not change spread.
Question 4 · 1.3
Of 240 randomly selected library visitors, 54 borrowed an audiobook. What proportion of the sample borrowed an audiobook?
- A0.180
- B0.540
- C0.225
- D0.450
Show the answer
C. The sample proportion is 54/240 = 0.225, or 22.5%. This describes the observed sample; the corresponding population proportion remains an unknown parameter.
Question 5 · 1.13
Forty volunteers are randomly assigned to two study methods. A significant score difference favors one method. What conclusion is supported by the assignment?
- AThe volunteers represent every student in the country
- BThe method caused a difference for the studied volunteers
- CThe sample was selected randomly from all students
- DEvery volunteer benefited by exactly the same amount
Show the answer
B. Random assignment supports attributing the observed treatment difference to the methods under the experimental conditions. Volunteer recruitment does not by itself justify generalization to all students.
Question 6 · 1.11
A school randomly selects 12 students from each of four grade levels. What is the sampling method?
- AA cluster sample of four grades
- BA convenience sample of 48 students
- CA census of the school population
- DA stratified random sample by grade
Show the answer
D. Grade levels are strata, and a random sample is taken within every stratum. Cluster sampling would select whole groups and include their members rather than sample within each grade.
How to study Unit 1
Take a small data set and calculate both mean/SD and median/IQR. Add one extreme value and compare which summaries move. Then describe the graph in a short paragraph that names the measured variable, units, shape and any unusual values.
For each study description, underline how participants were selected and circle how treatments were assigned. Write separate conclusions about generalization and causation. When diagnosing bias, describe the excluded or underrepresented group before predicting a direction.
Ashore's Stats course has a lesson and practice questions for every topic in this unit. The free starting check takes about 15 minutes and shows which ones are costing you points.
Find the Stats topics costing you points
The starting check takes about 15 minutes. Free, no card.
Starting check
SAT Math · 1 of 5
Calculator allowed
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