Recognize Statistical Questions

Lesson 1 of 5: Statistical Thinking

In this lesson:

• Tell statistical from non-statistical questions
• Identify population and attribute
• Rewrite vague questions to make them statistical

What You Will Learn Today

By the end of this lesson, you should be able to:

1. Define a statistical question as one that anticipates variability in the answers
2. Distinguish statistical questions from non-statistical questions in everyday lists
3. Identify the population a statistical question targets and the attribute under investigation
4. Rewrite a non-statistical or vague question to make it statistical

Which Question Needs a Survey?

Two questions about height:

• "How tall is the principal?"
• "How tall are the sixth graders in our school?"

Which one could you answer with a single measurement? Which one requires asking many people?

Two Lists Where Answers Differ

Five students' ages and sibling counts:

Variability Means Answers Differ Between People

Variability means the answers differ from one person to the next.

• One answer no matter who you ask: "What is 7 × 8?" → always 56
• Different answers from different people: "How many books did you read?"

Statistics is built to study the second kind.

Which Answer List Has Variability?

Three answer lists from a class survey:

• List A: 56, 56, 56, 56, 56
• List B: 11, 12, 11, 13, 11
• List C: "France", "France", "France", "France"

Pick the list with variability before advancing.

Questions That Anticipate Varying Answers

A statistical question anticipates variability in the answers.

• Expects different answers from different people
• Those varying answers are worth collecting and comparing

A non-statistical question expects one fixed answer, regardless of who answers.

One Diagnostic Test for Every Question

Before calling any question statistical, ask:

"Do we expect the answers to vary across the people we would ask?"

• Yes → statistical question
• No (same answer from everyone) → non-statistical

The test is answer variation — not grammar, length, or topic.

Apply the Diagnostic: Six Questions

Apply the Diagnostic on Your Own

Apply the diagnostic to these two questions:

1. "What day of the week is it?"
2. "How many hours of sleep did students get last night?"

For each: do the answers vary? Write before advancing.

Predict Before Advancing: Statistical or Not?

A student says: "'What year is it?' is statistical because we could ask 100 people."

Agree or disagree?

Think about whether those 100 answers would differ.

Respondent Count Is Not the Test

Same number of respondents, different answer patterns:

The test is answer variation, not respondent count.

Trap: One Person Gets One Answer

Consider this question: "What grade level am I in?"

Asked of a single student — statistical or non-statistical?

• Grade level does vary across the school
• But this question is asked about one student

What does the diagnostic say?

One person, one answer — non-statistical.

Classifying to Naming the Parts

You can classify questions. Now name the parts:

• Who is being asked or measured? → the population
• What is being measured or recorded? → the attribute

A complete statistical question names both.

Population and Attribute: Two Key Terms

• Population — the group the question is about
• Attribute — the characteristic being measured

Running example: "How tall are the sixth graders in our school?"

• Population: sixth graders in our school
• Attribute: height (in inches)

Same Attribute but Different Populations

Same attribute, different populations — different data sets:

Same attribute, different population — answers won't match.

Rewrite: Widen to a Group

Change one individual to a group — answers can now vary:

• "How tall is Maria?" → one person, non-statistical
• "How tall are the students in Maria's class?" → a group, statistical

The rewrite switches population from individual to group.

Rewrite: Specify Population and Attribute

Vague → statistical by naming who and what:

• "How much do people sleep?" → too vague: which people? what measure?
• "How many hours did our class sleep last night?" → clear who, clear what, answers vary

Who: our class. What: hours of sleep. When: last night.

Your Turn: Rewrite Two Questions

For each question below, rewrite it as a complete statistical question. Label the population and the attribute.

1. "How old is Mr. Johnson's dog?"
2. "How much do kids exercise?"

Write your rewrites, then compare — there are many valid versions.

Use All Three Boxes to Check

Every complete statistical question answers three questions:

Apply Three-Box Check to a Question

Does this question check all three boxes?

"How do students in our class feel about lunch?"

• WHO: students in our class ✓
• WHAT: feelings about lunch — is this a measurable attribute?
• VARIES: opinions vary ✓

What's missing or unclear?

Probe: Do Varying Opinions Make It Statistical?

"What is the best color?" is statistical — everyone has different opinions.

Agree or disagree? Apply the three-box check:

• WHO: which people? Unclear
• WHAT: "best" — is there a measurable attribute?
• VARIES: opinions differ ✓

Three Questions: No Help This Time

Answer all three before advancing:

1. "How old are the teachers at our school?" — classify and name population + attribute
2. "How many states are in the U.S.?" — classify; if non-statistical, rewrite it
3. Write your own statistical question about this classroom — label the population and attribute

What Makes a Statistical Question

✓ Answers vary across the group being asked

✓ Has a population (who) and an attribute (what)

✓ Rewrite: widen to a group or specify both parts

Many respondents ≠ statistical — answers must differ

Numerical answer ≠ statistical — "50 states" never varies

Next: Describing Those Varying Answers

6.SP.A.2 — Distributions

You can now identify a statistical question and know its answers will vary.

Next lesson: take those varying answers and describe them as a distribution — how they spread, where they cluster, what shape they form.

The heights example continues through the whole cluster.