Mission 19 · Unit 8

Statistical Questions

6.SP.A.1 · Unit 9
Today's objective: Recognize a statistical question and describe data variability.
Need a hint?
Re-read the problem and underline the numbers and the question. Pick one representation (model, table, or equation), show your steps, and check that your answer makes sense for the situation.

The student council wants to improve school lunches. They brainstormed 8 questions to survey students, but some questions will not give useful data because they have only one answer. Your team must sort the questions into statistical (expect variability) and non-statistical (only one answer), then write 2 original statistical questions the council should add to the survey.

LUNCH SURVEY Q1: How many students eat lunch? Q2: What is your favorite lunch? Q3: How old is our principal? Q4: How many snacks do you buy? Q5: What time does lunch start? Q6: How long do you wait in line? Q7: How many lunch tables are there? Q8: How do you rate the pizza? STATISTICAL NOT STATISTICAL

The Investigation

The Problem: Sort these 8 survey questions into two groups: statistical (answers will vary from person to person) and non-statistical (there is only one correct answer). For each question, explain WHY you placed it in that group. Then write 2 new statistical questions the student council should add.

The 8 Survey Questions

Statistical (Expect Variability)

Q2: What is your favorite school lunch?
Different students have different favorites. Answers vary.
Q4: How many snacks do you buy per week at school?
Each student buys a different amount. Data will spread out.
Q6: How many minutes do you wait in the lunch line?
Wait times change each day and per student. Variability exists.
Q8: On a scale of 1-5, how do you rate the school pizza?
Opinions vary. We expect a range of ratings.

Non-Statistical (One Answer)

Q1: How many students eat lunch at our school?
There is one specific number. No variability.
Q3: How old is our principal?
The principal has one age. Only one answer.
Q5: What time does lunch start?
Lunch starts at a set time. One answer for everyone.
Q7: How many lunch tables are in the cafeteria?
There is one correct count. No variability in answers.

Visual Model: The Variability Test

Decision Flowchart: Is It a Statistical Question? Read the question If I ask many people, will I get DIFFERENT answers? YES Statistical! NO Not statistical Key: Statistical questions expect VARIABILITY in the data collected.

Step-by-Step Investigation Guide

  1. Read each question carefully. Ask: "If I ask 30 students this question, will I get different answers?" Guiding question: Would everyone in class give the same response to Q5?
  2. Apply the variability test. If answers vary, the question is statistical. If there is one correct answer, it is not. Guiding question: For Q2 (favorite lunch), would all students say the same thing?
  3. Sort all 8 questions. Create a two-column chart: "Statistical" and "Non-Statistical." Place each question. Guiding question: Which column do you expect to have more questions?
  4. Write your reasoning. For each question, explain in one sentence why you placed it in that column. Guiding question: Can you use the word "variability" in your explanation?
  5. Write 2 new statistical questions. These should help the student council learn about lunch preferences. Guiding question: What would the council need to know to make lunch better?
  6. Predict the data. For one of your new questions, predict what the answers might look like. Would they be spread out or clumped together? Guiding question: How does anticipating variability help you plan a survey?

Language Support: Key Vocabulary

Statistical question
A question where you expect to get different answers from different people. The data will vary.
Non-statistical question
A question with only one correct answer. No variability.
Variability
How much data values are different from each other. Spread.
Survey
A set of questions asked to many people to collect data.
Data
Information collected from observations or questions. Numbers or categories.
Predict
Make a guess about what will happen based on what you know.
Sentence Frames:

"This is a statistical question because if I ask many people, I will get _____."

"This is NOT statistical because there is only one answer: _____."

"I expect variability because different students will _____."

Multiple Representations

Approach 1: The "30 Students" Test

Imagine asking 30 students. Write down what you think the first 5 answers would be. If they are all the same, it is non-statistical. If they differ, it is statistical.

Approach 2: Sorting Chart

Create a T-chart. Left side: "Answers vary" (statistical). Right side: "One answer" (non-statistical). Place each question card on the correct side.

Approach 3: Rewrite Strategy

Take a non-statistical question and rewrite it to make it statistical. Example: "What time does lunch start?" becomes "What time do YOU start eating lunch?" Now answers will vary!

Team Roles

Facilitator Read each question aloud to the team. After sorting, make sure every member agrees on the placement. Manage time.
Model Builder Create the two-column sorting chart on paper. Write each question in the correct column. Draw the flowchart decision process.
Precision Checker For each placement, ask: "Are you sure? Could answers vary?" Check that the reasoning sentence uses the word "variability" or explains why answers do/do not change.
Reporter Prepare the defense: explain the sorting rule, share the 2 new questions, and present the team's reasoning for the trickiest question.

Timed Lab Phases

Launch Phase
03:00

Read the student council scenario. Assign roles. Discuss what makes a question statistical.

  • What does "variability" mean?
  • Give one example of a question where answers would vary.
  • Give one example where there is only one answer.
Checkpoint: Everyone can explain the difference between statistical and non-statistical in their own words.

Sort all 8 questions. Write one sentence of reasoning for each.

  • Read each question and apply the "30 students" test.
  • Place in the correct column of your chart.
  • Write: "This IS/IS NOT statistical because _____."
Checkpoint: All 8 questions sorted with reasoning written for each.

Write 2 new statistical questions. Predict what the data might look like.

  • What topic would help the council improve lunch?
  • Is your question one that will get different answers?
  • Predict: would answers be spread out or clumped together?
Checkpoint: 2 new statistical questions written with variability predictions.

Reporter prepares the defense. Identify the trickiest question and explain your team's reasoning.

  • "Our sorting rule is: if _____, then it is statistical."
  • "The trickiest question was Q___ because _____."
  • "Our two new questions are _____ and _____."
Checkpoint: Defense includes sorting rule, trickiest question explanation, and new questions.

Challenge Extensions

Extension Problem: Take non-statistical question Q5 ("What time does lunch start?") and rewrite it THREE different ways to make it statistical. For each rewrite, explain what kind of variability you would expect in the answers.

What If?

  • Is "How tall are 6th graders?" statistical? What about "How tall is the tallest 6th grader?"
  • Write a question that LOOKS statistical but is actually non-statistical. Can you trick another team?
  • If you surveyed 100 students with Q8 (pizza rating 1-5), predict how many would give each rating. Sketch a bar graph.

Real-Life Connections

Statistical questions drive real surveys: product reviews, election polls, medical studies, sports analytics, and school improvement plans all start with well-crafted statistical questions.

Defense Preparation

  1. What is a statistical question? Give the definition in your own words.
  2. Why is Q3 ("How old is our principal?") not statistical?
  3. Which question was hardest to sort? Why?
  4. Share your 2 new questions. Why are they statistical?
Sentence Starters:
  • "A statistical question is one where _____."
  • "Q___ is not statistical because the answer is always _____."
  • "Our new question expects variability because _____."

Rubric

Criteria Excellent (4) Proficient (3) Developing (2)
Sorting accuracy All 8 correct with reasoning 7-8 correct, partial reasoning 5-6 correct
Reasoning quality Uses "variability" language for all Most explanations clear Some explanations present
New questions 2 strong statistical questions with predictions 2 questions, one prediction 1 question written
Defense Clear rule + trickiest question analysis Rule stated, some analysis Partial defense

Exit Product

Your team submits: A Survey Question Analysis Sheet with:
  • A two-column sorting chart (Statistical vs. Non-Statistical)
  • All 8 questions placed correctly
  • One sentence of reasoning for each question
  • 2 new statistical questions the council should add
  • A variability prediction for at least one new question
  • A one-sentence definition of "statistical question"

Self-Assessment Checklist