From a Topic to a Question Data Can Answer
A topic is not yet an investigative question. “Later school start times” could lead to questions about students’ opinions, their sleep, or what a school should do. Those questions are not interchangeable: the kind of answer sought determines what data would be relevant.
In the previous tutorial, Mixed Practice: Comparing Distributions in Context, you used data displays to describe and compare groups. Before there can be a useful display or comparison, someone must decide what to observe and ask. A well-framed statistical question makes that task clearer by identifying what information matters and recognizing that responses may differ from one person or observation to another.
Variability means that observations are not all expected to be identical. If a question asks about students’ nightly sleep, for example, students may report different amounts. A statistical investigation can summarize that variation with appropriate displays or statistics, such as the mean and standard deviation or the median and IQR, as introduced earlier in this course.
A statistical question does not have to ask for a number directly. It may ask about a categorical variable, such as whether each student supports a schedule change. If responses vary across students, the collected answers can be summarized—for example, by counting the responses in each category or calculating a proportion. The important point is that the question invites data from multiple observations and asks about a pattern or summary, rather than treating one person’s response as the whole answer.
Opinion Questions, Yes/No Questions, and Statistical Questions
An opinion question asks what someone believes, prefers, or thinks should happen. Opinion data can be collected and summarized, but a response to an opinion question does not by itself answer an objective question about a measurable outcome. For example, a survey can show how many students favor a later start. It cannot establish from those opinions alone whether students would sleep longer under a different schedule.
A yes/no question is not automatically unstatistical. Consider “Do you support a later start time?” asked once to one student. That gives one person’s yes-or-no opinion. Asked consistently of many students, it produces a set of responses that may vary. “What proportion of students in the survey support a later start time?” is statistical because it asks about a pattern across responses.
The same distinction applies to factual yes/no questions. “Did this student arrive late today?” is a question about one student on one day. “On what proportion of school days were students in this group late?” asks about repeated observations, where the answers may vary. The wording alone does not determine whether a question is statistical; consider the observations it calls for and the variation they may show.
A question may also be vague or difficult to answer even if it sounds factual. Words such as “better,” “healthier,” and “more rested” need clarification: What will be observed or recorded to represent that idea? A useful question points toward a variable that can be collected in a consistent way.
A Practical Question Audit
Before collecting data, use a short audit. It helps turn a broad interest into a question that is focused enough to investigate. You do not need to write a long research plan at this stage. The goal is to make the requested information and the relevant observations clear.
Who or what will provide the data—for example, students, school days, or recorded sleep periods?
State what will be recorded, such as hours of sleep, a rating on a defined scale, or support versus opposition.
Ask whether different students, days, or observations could give different values or categories.
Make sure the proposed data could answer the question as written. A survey of preferences answers a question about preferences, not a question about actual sleep.
This audit also helps expose questions that combine several issues. “Should school start later because students are tired and their grades are low?” includes a policy judgment, a claim about tiredness, and a claim about grades. A single answer would not tell you which part is being addressed. A focused investigation chooses a specific question and identifies the variable needed to answer it.
Worked Example: Separate Opinion from Measurable Outcome
Worked Example: Separate Opinion from Measurable Outcome
A student group is discussing whether school should begin later. Consider these three possible questions:
- “Should our school start later?”
- “Do you support moving the start time later?”
- “How many hours did students sleep on school nights during the past week?”
Classify each question. The first asks for a policy judgment. It could prompt reasons or opinions, but there is no single measurement that makes one answer objectively correct. It is not, as written, a statistical question about a measurable outcome.
The second asks an individual for an opinion with a yes-or-no response. Asked of one student, it is not asking about variation across observations. Asked consistently of many students, it produces categorical data that can vary. A statistical version is: “What proportion of students who respond to the survey support moving the start time later?” That question asks for a summary of varied responses. It describes support among the respondents; it does not establish what a later schedule would do to sleep.
The third question identifies a measurable variable: hours of sleep on school nights during a specified past week. Students’ reported values may differ, so a group’s responses can be summarized. To make the wording still more explicit, ask: “Among students in the survey, how many hours of sleep did each report getting on school nights during the past week?” This points to one observation per student and a defined time period.
Conclusion. The first question seeks a judgment, the second can produce statistical data when asked across a group but measures opinion, and the third asks about a measurable outcome that can vary. Keeping those purposes separate prevents a survey about what students favor from being mistaken for evidence about how much they sleep.
Worked Example: Revise a Vague Question About Being Rested
Worked Example: Revise a Vague Question About Being Rested
A school committee proposes the question, “Would students be more rested if school started later?” The phrase “more rested” is not defined, and the question asks respondents to predict a hypothetical effect. Their answers alone cannot establish whether a later start would make students more rested.
Clarify what can be measured. One possible variable is a student’s self-reported alertness rating during first period. The committee could define a scale—for example, 1 for “not at all alert” and 5 for “very alert”—and ask students to give a rating on specified school days. Because ratings may differ across students and days, the responses could be summarized.
A more answerable descriptive question would be: “What are the first-period alertness ratings reported by students at this school during the current school week?” It names the variable, the setting, and the time period. Data collected for this question describe reported ratings during that week; they do not answer what would happen under a schedule that has not been used.
If the committee is interested in students’ predictions, it can ask a separate opinion question: “How do you think a later start time would affect your first-period alertness?” Responses could be categorized or summarized as opinions. The interpretation must remain limited to what respondents predict. These answers are not observations of actual alertness under a later schedule.
Conclusion. The original question mixes a hypothetical prediction with an undefined outcome. Separating a measurable report of current alertness from opinions about a possible schedule makes the evidence and its limits clear.
Worked Example: Make a Yes/No Question Statistical
Worked Example: Make a Yes/No Question Statistical
A school wants to learn whether students support a proposed 8:45 a.m. start time. The initial question is “Do you support an 8:45 start?” It is clear as an individual survey item, but the investigative question should say what will be learned from the group’s responses.
Specify the response and summary. Suppose each responding student selects “support” or “do not support.” The variable is support for the proposed start time, with two categories. Different students may choose different categories. A statistical question based on the item is: “What proportion of students who complete the survey support an 8:45 a.m. start time?”
Check that the data match. The response options directly record support or lack of support, so the answers can be counted by category. The proportion supporting the proposal can be found by dividing the number of “support” responses by the total number of responses. That result describes the students who completed the survey. It does not measure sleep, alertness, academic performance, or whether the schedule should be adopted.
Conclusion. Yes/no format is compatible with a statistical investigation when responses are collected across multiple observations and the question asks about their distribution or a summary. The statistical question here concerns support among survey respondents, not the effects of a later start.
Common Mistakes and AP Exam Tips
- Treating every yes/no item as nonstatistical. A single yes/no answer is one response. Across many people or repeated occasions, yes/no responses can vary and can be summarized. State what group of responses the question asks about.
- Treating an opinion as evidence of an outcome. Students’ support for a later start describes their preferences. It does not show that the schedule would increase sleep or alertness.
- Assuming a likely outcome in a hypothetical question. “Would students be more rested if school started later?” asks respondents to predict a hypothetical effect; it does not assert that the effect is likely. Their answers alone cannot establish whether a later start would make students more rested.
- Using a vague variable. “More rested” or “better” needs an observable definition. Identify a measure, such as reported sleep hours or a specified alertness rating, and state when it is recorded.
- Asking about one observation but drawing a group conclusion. One student’s response cannot describe all students. A question about a group needs observations from multiple members of that group.
- Claiming more than the data answer. A survey of reported sleep can describe those reports. A survey of opinions can describe opinions. In a full-credit response, match the conclusion to the variable actually collected.
For a clear AP Statistics answer, identify whether the question asks for an opinion or a measurable variable, explain whether responses may vary across observations, and say what data would answer it. If revising the question, specify the variable and relevant time or setting. Do not claim that one kind of data answers a different question.
Check Your Understanding
For each item, decide what information the question seeks and whether it could be answered statistically. Explain what data would be relevant.
- “Should our school start later?” Is this a measurable statistical question as written, or a judgment? Explain.
- A survey asks 200 students whether they support an 8:45 a.m. start. Write a statistical question that could be answered using these yes/no responses.
- “Would students be more rested if school started later?” What does this ask respondents to do, and what can their answers alone establish?
- Revise “Are students alert?” into a question that identifies a measurable variable and a time or setting.
- A survey asks students how many hours they slept last night. What variable is recorded, and why might a question about responses from many students be statistical?