Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.1

Lesson 2.1Understand Statistical Questions

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can tell the difference between a statistical question and a non-statistical question.

Why This Matters You've just been hired as the data analyst for a youth basketball league. The head coach hands you a list of questions the staff wants to investigate about their players. Some questions will give you interesting data with variety, while others have just one fixed answer. Your job: figure out which questions are worth investigating with data. Two of the coach's questions are: "How tall is our point guard?" and "How tall is each player on the roster?"

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Statistical QuestionSpanish: Pregunta estadística A question answered with data that are expected to vary. How tall is each student?
Non-statistical QuestionSpanish: Pregunta no estadística A question that does not anticipate variability in the data used to answer it. It may ask for one fact or measurement. How tall is the flagpole?
DataSpanish: Datos Facts and numbers you collect, like answers to a survey. 0, 2, 5, 1 pets
VariabilitySpanish: Variabilidad How spread out the numbers are. 0, 2, 5 pets — answers vary
SurveySpanish: Encuesta Collecting facts by asking people questions. Asking classmates one question
Data distributionSpanish: Distribución de datos How the data looks: where it sits and how spread out it is. A distribution is symmetric when its left and right sides have approximately matching shapes around the center.

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Which is statistical: “How many siblings does each student have?” or “How many sides does a triangle have?”

  1. Sibling counts differ: 0, 1, 3.
  2. A triangle always has 3 sides.

Answer: The sibling question is statistical; the triangle question is not.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

New question: "How many pets does each student in our class have?" Will every student give the same answer, or different answers?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • This question statistical because .
  • I expect the answers to from person to person.
  • A non-statistical question has answer.
  • The data I would collect might look like .

Word bank statisticalnon-statisticalvariabilitydatasurveyvaryanswerscollectfixeddifferentquestiontypical

Watch out!A common mistake

A common mistake in Statistical Questions and Data is judging a question by its topic or its numbers instead of its variability. Students see a question about ONE player, ONE game, or ONE fixed fact

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.1

Lesson 2.1Understand Statistical Questions

Level 0Most support · every hint printed

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can tell the difference between a statistical question and a non-statistical question.

Why This Matters You've just been hired as the data analyst for a youth basketball league. The head coach hands you a list of questions the staff wants to investigate about their players. Some questions will give you interesting data with variety, while others have just one fixed answer. Your job: figure out which questions are worth investigating with data. Two of the coach's questions are: "How tall is our point guard?" and "How tall is each player on the roster?"

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Which is statistical: “How many siblings does each student have?” or “How many sides does a triangle have?”

  1. Sibling counts differ: 0, 1, 3.
  2. A triangle always has 3 sides.

Answer: The sibling question is statistical; the triangle question is not.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each question to its type.

    1. How tall is each swimmer on the team?
    2. What color is the team mascot?
    3. How many laps does each runner complete?
    4. How many players are on a soccer team?
    • AStatistical
    • BNot Statistical
    • CStatistical
    • DNot Statistical
    Steps to try
    1. Read each question on the left and underline the word 'each' when you see it — it's a clue that many people are being measured.
    2. Sort by asking: does this question collect data from many individuals (varies), or state one fact with a single answer (doesn't vary)?
    3. Start with 'What color is the team mascot?' — one mascot, one color, so match it to Not Statistical. Do the rest one question at a time.
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Which of the following is a statistical question?

    1. AHow many points did each player score this season?
    2. BHow many points are scored for a free throw?
    3. CWhat sport does this team play?
    4. DHow many halves are in a soccer game?
    Steps to try
    1. Re-read each question and ask: would different people or games give different answers, or is there just one fixed answer?
    2. A statistical question expects variability — many answers that differ. Sort each choice into 'one fixed answer' or 'answers that vary'.
    3. Test one: 'How many halves are in a soccer game?' Every game has the same number — no variability there. Check the other three the same way.
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    Which question is NOT a statistical question?

    1. AHow many home runs did each player hit this year?
    2. BHow many miles does each runner train per week?
    3. CHow many innings are in a baseball game?
    4. DHow tall is each player on the basketball team?
    Steps to try
    1. Careful — this asks for the question that is NOT statistical: the one with a single fixed answer instead of varying data.
    2. For each choice ask: 'Would each player or runner give a different number?' The odd one out is a rule of the game, not data you collect.
    3. Start with 'How tall is each player?' — heights differ player to player, so that one IS statistical. Keep testing until one has just one answer.
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Why is 'How many hours of sleep did each student get last night?' a statistical question?

    1. ABecause different students got different amounts of sleep
    2. BBecause it asks about sleep
    3. CBecause hours are numbers
    4. DBecause it asks every student the same question
    Steps to try
    1. The question asks WHY it's statistical — focus on what happens when many students answer, not on the topic of sleep.
    2. Think: if you asked every student how long they slept, would you get one number or many different numbers? That idea is called variability.
    3. Picture asking 5 classmates their sleep hours and listing the numbers. Notice whether the list is all the same or varied — that's the key idea.
    Show your work

Explain your thinkingWhat pattern do you notice about statistical questions compared to non-statistical questions?

Sentence starter Statistical questions expect ___ in the answers because ___. Non-statistical questions have only ___ answer because ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help