AP Statistics Formulate Questions is the practice of writing a clear investigative question that a statistical study can actually answer. Your job is to take a real-world situation and turn it into a question about data, variability, or a relationship that you can study with sampling, experiments, probability, or inference.

This practice covers one subskill, Skill 1.A: determine a valid investigative question that requires a statistical investigation. It shows up on both multiple-choice and free-response questions, and it sets up everything else you do in the course. A good question points you toward the right data and the right analysis.

What Formulate Questions Means

An investigative question is one that you answer by collecting and analyzing data, not by looking up a single fact or doing one arithmetic calculation.

The key word is "statistical." A statistical question anticipates variability. It expects that values will differ across people, objects, or repeated measurements, and it asks something about that variation, a typical value, or a pattern.

Compare these two:

Not statistical: "How tall is the teacher in room 204?" There is one answer.
Statistical: "What is the typical height of seniors at our school, and how much do heights vary?" Answers vary across students, so you need data.

Formulating a question well means the question is specific, answerable with data, and matched to the population, treatments, or relationship you care about.

What This Practice Requires

To do this well, you need to be able to:

Recognize when a question can be answered by gathering and analyzing data.
Tell the difference between a question with a single answer and a question that involves variability.
Identify the variable or variables the question is about and whether they are categorical or quantitative.
Match the question to a study type, such as a survey for an estimate, an experiment for cause and effect, or a regression for a relationship between two quantitative variables.
Make sure the question names a clear population or group so a conclusion has meaning.

Subskills You Need

Skill 1.A: Determine a valid investigative question that requires a statistical investigation.

A valid investigative question has a few features:

It anticipates variability in the data.
It can be answered by collecting data, not by a single fact.
It is specific about the group, variable, or relationship being studied.
It connects to a method you could actually carry out.

Ask yourself: "Would different individuals or repeated trials give different answers?" If yes, the question is statistical. "Could I answer this with one measurement or one lookup?" If yes, it is not an investigative question.

How It Shows Up on the AP Exam

Skill 1.A appears in both multiple-choice and free-response sections.

On multiple choice, you might:

Pick which question requires a statistical investigation.
Identify which question matches a described study or data set.
Recognize a question that anticipates variability versus one with a single answer.

On free response, you might:

Write or refine an investigative question for a given context.
Explain why a question can be answered with the data collected.
State the question that a study is designed to address.

Practical tip: read the prompt and name the task before you write. Make sure your question matches the population and variables in the scenario, and keep it specific enough that a reader knows exactly what data would answer it.

Examples Across the Course

Formulating questions connects to every part of the course. Here are varied examples tied to different content areas.

Exploring one-variable data "How much do daily commute times vary among workers in our city, and what is a typical commute time?" This anticipates variability and points to a distribution you can summarize and graph.

Exploring two-variable data and regression "Can the number of cricket chirps per minute predict the air temperature?" This asks about a relationship between two quantitative variables, which sets up correlation and a linear regression model.

Collecting data with experiments "Does a new study technique improve test scores compared to the usual technique for students in this course?" This is a cause-and-effect question, so it points to a randomized experiment with treatment groups.

Probability and random variables "About how many rolls of a fair six-sided die should we expect before getting three 1s?" This question anticipates variation across trials and connects to simulation and probability distributions.

Inference for proportions "What proportion of voters in this district support the ballot measure, and how confident can we be in that estimate?" This points toward random sampling and a confidence interval for a population proportion.

Notice how each question names a group or relationship, expects variability, and suggests a specific method.

How to Practice Formulate Questions

Take any everyday claim and rewrite it as a statistical question. Add a group, a variable, and the idea of variability.
Sort questions into "single answer" versus "needs data." Explain your reasoning each time.
For every question you write, name the population, the variable or variables, and a study type that could answer it.
Practice matching: given a data set or study description, write the question it answers.
When you revise a vague question, make it more specific by adding who, what variable, and what comparison or estimate.

Common Mistakes

Writing a question with a single answer, like asking about one specific object instead of a group.
Leaving out the population, so the conclusion has no clear meaning.
Being too vague, like "Is exercise good?" instead of naming a variable and a comparison.
Asking a cause-and-effect question but planning only a survey, which cannot establish causation.
Confusing categorical and quantitative variables, which leads to a question that does not match the data.
Turning a statistical question into a yes or no lookup that does not involve variability.

Quick Review

An investigative question is answered by collecting and analyzing data.
A statistical question anticipates variability and is specific about the group and variable.
Skill 1.A asks you to determine a valid question that requires a statistical investigation.
Good questions match a method: surveys for estimates, experiments for cause and effect, regression for relationships between quantitative variables.
On the exam, keep questions specific, tie them to the population in the prompt, and make sure they could actually be answered with data.