Recognizing Statistical Questions

In this lesson:

• Define a statistical question and identify variability
• Distinguish statistical from non-statistical questions
• Revise non-statistical questions into statistical ones

Our Learning Objectives for Today

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

1. Define a statistical question — one that expects different answers from different individuals and accounts for variability
2. Distinguish statistical from non-statistical questions (non-statistical ones have a single definite answer)
3. Revise non-statistical questions into statistical ones

What Makes a Question Statistical?

Consider these two questions:

• "How old am I?" — one person, one answer
• "How old are the students in my school?" — many students, many answers

Which question would you need to collect data to answer?

What Is a Statistical Question?

A statistical question is one where you collect data from multiple instances and expect the answers to vary.

• Variability is not a problem — it is the point
• The answer describes a distribution, not one number
• Different people or instances give different answers

Apply the Variability Test to Classify

Does asking multiple people or instances give different answers? Yes → Statistical. No → Not statistical.

What Makes a Question Non-Statistical?

A non-statistical question has one specific, definite answer. No data collection across many instances is needed.

• "How old am I?" — one person, one age
• "How tall is the Eiffel Tower?" — one measurement, always the same
• "What is 6 × 7?" — one answer: 42

Quick Check: One Question to Classify

Is this question statistical or non-statistical?

"How many students are in this classroom right now?"

Think for a moment — apply the variability test before the next slide...

Example: "How Tall Is the Eiffel Tower?"

Question: How tall is the Eiffel Tower?

Apply the test: Is there variability in the answer?

• The Eiffel Tower has one specific height
• Measuring it again would give the same value
• No population, no variation

Verdict: Non-statistical — one definite measurement

Example: "How Tall Are Students in This Class?"

Question: How tall are students in this class?

• Different students have different heights
• You'd need to measure everyone to answer it
• The answer is a range — not a single number

Example: "What Is 6 × 7?"

Question: What is 6 × 7?

Apply the test: Does this question involve a population? Will different instances give different answers?

• 6 × 7 = 42. Always. For everyone.
• This is a computation — not data collection
• Numbers alone do not make a question statistical

Verdict: Non-statistical

Example: Homework Hours per Week

Question: How many hours per week do students in this school spend on homework?

Apply the test:

• Different students study for different amounts of time
• You'd need to survey many students
• Answers will vary — that variation is the data

Verdict: Statistical

Pause and Classify These Three Questions

Label each question statistical (S) or non-statistical (N):

1. "What temperature is it outside right now?"
2. "What temperatures do we experience in this city in January?"
3. "How many pages does this book have?"

Apply the variability test — then advance for answers.

Answers to the Classification Practice

1. "What temp is it outside right now?" → N (one value, no variability)
2. "What temps do we see in this city in January?" → S (many days, temperatures vary)
3. "How many pages does this book have?" → N (one book, one page count)

How did you do?

How to Revise Non-Statistical Questions

Revise by changing the scope: from one specific instance to a population.

Strategy: Replace the one specific instance with a group

• "I" → "students in our school"
• "this book" → "books that won the Newbery Award"

Widening scope introduces variability and creates a statistical question.

Revision Example 1: Sleep Hours

Original (non-statistical): How many hours did I sleep last night?

• One person, one night — one answer

Revised (statistical): How many hours per night do 6th graders typically sleep?

• Many students, many nights — different answers
• Now requires data collection from a population

Revision Example: Temperature into Population

Original (non-statistical): What temperature is it outside right now?

• One moment in time — one answer

Revised (statistical): What temperatures do we experience in this city in January?

• Many days, varying temperatures — different answers
• Requires measuring or recording data over time

Revision Example 3: Book Pages

Original (non-statistical): How many pages does this book have?

• This specific book — one answer

Revised (statistical): How many pages are in books that won the Newbery Award?

• Many books, varying lengths — different answers
• Requires collecting data from many books

Watch Out: Uncertain Does Not Mean Statistical

"Will it rain tomorrow?" — Is this statistical?

• Uncertainty ≠ statistical; one unknown event is not a population
• This refers to one specific event — one tomorrow
• One event ≠ population; no variability across instances

Statistical version: "How many rainy days per year does our city get?"

Your Turn: Classify and Revise Each

Classify as S (statistical) or N (non-statistical). Revise the non-statistical ones.

1. "How fast do cars drive on this street?"
2. "How many siblings does Marcus have?"
3. "How much do backpacks in this school weigh?"

Try all three — then advance.

Answers: Classify and Revise Practice

1. Car speeds → S (speeds vary by car and time; data from measurement)
2. Marcus's siblings → N → Revised: "How many siblings do students in this class have?"
3. Backpack weights → S (different loads, weights vary)

Notice: questions 1 and 3 use measurements — not surveys.

Key Takeaways from This Lesson

• Statistical questions anticipate variability — answers differ across instances
• Non-statistical questions have one definite answer
• Revise: expand scope from one instance to a population
• Watch: Numbers ≠ statistical (math facts have one answer)
• Watch: Uncertain ≠ statistical (one event ≠ population)
• Watch: Data comes from measurements, not only surveys

What's Coming in the Next Lesson

6.SP.A.2 — Describing the Distribution of a Data Set

You can now recognize statistical questions. Next, we explore what collected data looks like:

• Datasets have a distribution — spread across values
• We describe distributions using center, spread, and shape