Statistical Questions

Grade 6 · statistics · 101 practice problems · read aloud

🔊 Listen to this explanation

Statistical Questions: What Are They?

A statistical question is one that can be answered by collecting data that varies (has more than one possible answer). It asks about a group, not just one person or thing. We use them to understand trends and patterns in the world! 📊

How to Identify a Statistical Question

  1. Ask: "Does this question have a single, fixed answer?"
  2. If YES: It is NOT a statistical question.
  3. If NO: "Would the answers vary when asked of different people or things?"
  4. If YES: It IS a statistical question!

Visual Examples

Example 1: "How tall is the school principal?"

  • This has one, fixed answer. It's a specific measurement.
  • Verdict: NOT a statistical question.

Example 2: "What are the heights of the 6th-grade students in my school?"

  • This would have many different answers. You would collect data from many students.
  • You could make a dot plot or find the average height from the data.
  • Verdict: THIS IS a statistical question.

Example 3: "How many pets does each student in my class have?"

  • Answers will vary! Some have 0, some have 2, some have 1.
  • You can collect all the answers and analyze the data.
  • Verdict: THIS IS a statistical question.

🚨 Common Mistakes

  • Confusing "how many" questions: "How many sisters do I have?" is NOT statistical (it's about one person). "How many sisters do students in this class have?" IS statistical (answers vary).
  • Forgetting about variation: If the answer doesn't change, it's not statistical. Think: "Would we get a list of different numbers or answers?"

💡 Tips & Tricks

  • The "Ant" Test: If you could ask an ant your question and it could point to one answer, it's NOT statistical. If the ant would be confused because there are many answers, it IS statistical.
  • Look for "each" or "all": Questions that ask about "each student" or "all the trees" are often statistical because they involve a whole group.

How to Practice

Try these activities to become a statistical question expert:

  • Question Sort: Write 10 questions on sticky notes. Sort them into two piles: "Statistical" and "Not Statistical."
  • Make Your Own: Look around your classroom. Can you write one statistical question about the books, and one that is not statistical?
  • Real-World Detective: Listen to conversations or read news headlines. When you hear a question, ask yourself, "Is that statistical?"

Practice problems

6 of the 101, worked through step by step — try them before opening the answer.

1 3² + 4² - √25 = ?

Hint: Remember to calculate exponents first, then find the square root, and finally perform the addition and subtraction in order.

Show the answer

Answer: 20

  1. Calculate 3 squared. 3² means 3 × 3 = 9.
  2. Calculate 4 squared. 4² means 4 × 4 = 16.
  3. Add the results from Step 1 and
  4. 9 + 16 = 25.
  5. Calculate the square root of 25. √25 = 5.
  6. Subtract the result of Step 4 from the result of
  7. 25 − 5 = 20. Final Answer: 20

Let's solve step by step.

2 3² × (4 + 6) ÷ 2 = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication and division from left to right.

Show the answer

Answer: 45

  1. Handle the exponent. 3² means 3 × 3 = 9 So now we have: 9 × (4 + 6) ÷ 2
  2. Evaluate inside the parentheses. 4 + 6 = 10 So now we have: 9 × 10 ÷ 2
  3. Multiplication and division from left to right. First: 9 × 10 = 90 Then: 90 ÷ 2 = 45 Final Answer: 45

Let's solve the problem step by step using the order of operations (PEMDAS/BODMAS). We have: 3² × (4 + 6) ÷ 2

3 3² × (15 - 7) ÷ 4 = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication and division from left to right.

Show the answer

Answer: 18

  1. Handle the exponent (power). 3² means 3 × 3, which is 9. So the expression becomes: 9 × (15 - 7) ÷ 4
  2. Evaluate the expression inside the parentheses. 15 - 7 = 8 So the expression becomes: 9 × 8 ÷ 4
  3. Perform multiplication and division from left to right. First, do the multiplication: 9 × 8 = 72 Now the expression is: 72 ÷ 4
  4. Perform the division. 72 ÷ 4 = 18 Therefore, the final answer is 18.

Let's solve the problem step-by-step using the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division from left to right, Addition and Subtraction from left to right). The problem is: 3² × (15 - 7) ÷ 4

4 3² × (12 - 8) ÷ 2 = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication and division from left to right.

Show the answer

Answer: 18

  1. Solve inside the parentheses: 12 - 8 = 4
  2. Calculate the exponent: 3² = 9
  3. Multiply: 9 × 4 = 36
  4. Divide: 36 ÷ 2 = 18

The answer is 18.

5 3² × (18 - 6) ÷ 4 = ?

Hint: Remember to follow the order of operations - parentheses first, then exponents, then multiplication and division from left to right.

Show the answer

Answer: 27

  1. Start with the expression: 3² × (18 - 6) ÷ 4
  2. Solve inside the parentheses first: 18 - 6 = 12
  3. Now we have: 3² × 12 ÷ 4
  4. Calculate the exponent: 3² = 9
  5. Now we have: 9 × 12 ÷ 4
  6. Multiply and divide from left to right: 9 × 12 = 108
  7. Then: 108 ÷ 4 = 27

The answer is 27.

6 3² × (18 - 12) ÷ 2 = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication and division from left to right

Show the answer

Answer: 27

  1. Start with the expression: 3² × (18 - 12) ÷ 2
  2. Solve inside the parentheses first: 18 - 12 = 6
  3. Now we have: 3² × 6 ÷ 2
  4. Calculate the exponent: 3² = 9
  5. Now we have: 9 × 6 ÷ 2
  6. Multiply and divide from left to right: 9 × 6 = 54
  7. Then: 54 ÷ 2 = 27
  8. The final answer is 27
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