Statistical Questions

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Statistical Questions · Grade 6 · Worksheet 3

1. Which question is statistical: 'How many books does Kaia read in a month?' or 'How many books does Aroha read in a month?' Explain why. Answer: Both questions are statistical because the number of books read can vary from month to month for each person. Solution: Analyze the first question: 'How many books does Kaia read in a month?' This question is about a single person, Kaia. However, the number of books Kaia reads can change from month to month (e.g., 2 books one month, 5 books another month).
   Full step-by-step solution

   Step 1: Understand the definition of a statistical question: A statistical question is one that anticipates variability in the data related to the question. Step 2: Analyze the first question: 'How many books does Kaia read in a month?' This question is about a single person, Kaia. However, the number of books Kaia reads can change from month to month (e.g., 2 books one month, 5 books another month). So, there is variability over time, making it a statistical question. Step 3: Analyze the second question: 'How many books does Aroha read in a month?' Similarly, this is about a single person, Aroha. The number of books Aroha reads can also vary from month to month, so it is also a statistical question. Step 4: Conclusion: Both questions are statistical because they anticipate variability (the number of books can change each month). The answer is that both are statistical.

2. 3² × (12 - 8) ÷ 2 = ? Answer: 18 Solution: Solve inside the parentheses: 12 - 8 = 4 Calculate the exponent: 3² = 9 Multiply: 9 × 4 = 36 Divide: 36 ÷ 2 = 18 The answer is 18.
   Full step-by-step solution

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

3. Aroha is considering the following two questions about her classmates: 1. How many pets does each student in my class have? 2. How many pets does my friend Tane have? Which question is a statistical question, and why? Explain by identifying whether the answers would show variability. Answer: Question 1 is statistical; Question 2 is not. Solution: A statistical question is one that anticipates variability in the data collected. Question 1 asks about 'each student in my class' — different students likely have different numbers of pets, so the answers will vary.
   Full step-by-step solution

   Step 1: A statistical question is one that anticipates variability in the data collected. Step 2: Question 1 asks about 'each student in my class' — different students likely have different numbers of pets, so the answers will vary. Therefore, Question 1 is a statistical question. Step 3: Question 2 asks about 'my friend Tane' — this refers to one specific person, so there is only one answer. There is no variability. Therefore, Question 2 is not a statistical question. Final answer: Question 1 is statistical because it expects varying numbers of pets across students; Question 2 is not statistical because it asks about a single individual.

4. Which question is statistical: 'How many books did Sophia read last month?' or 'How many books did students in Grade 6 read last month?' Explain why. Answer: 'How many books did students in Grade 6 read last month?' is statistical because it anticipates variability in the number of books read among different students. Solution: Identify the first question: 'How many books did Sophia read last month?' This asks about one specific person, so the answer is a single number (e.g., 3 books). There is no variability.
   Full step-by-step solution

   Step 1: Identify the first question: 'How many books did Sophia read last month?' This asks about one specific person, so the answer is a single number (e.g., 3 books). There is no variability. Step 2: Identify the second question: 'How many books did students in Grade 6 read last month?' This asks about a group of students, and each student likely read a different number of books. The answers will vary (e.g., 1, 5, 2, 7, etc.). Step 3: A statistical question is one that anticipates variability in the data collected. Since the second question expects different answers from different students, it is statistical. The first question is not statistical because it has only one answer. The answer is: 'How many books did students in Grade 6 read last month?' is statistical.

5. 3² × (4 + 6) ÷ 2 = ? Answer: 45 Solution: 3² × (4 + 6) ÷ 2 Handle the exponent. 3² means 3 × 3 = 9 So now we have: 9 × (4 + 6) ÷ 2 Evaluate inside the parentheses. 4 + 6 = 10 So now we have: 9 × 10 ÷ 2 Multiplication and division from left to right.
   Full step-by-step solution

   Let's solve the problem step by step using the order of operations (PEMDAS/BODMAS). We have: 3² × (4 + 6) ÷ 2 Step 1: Handle the exponent. 3² means 3 × 3 = 9 So now we have: 9 × (4 + 6) ÷ 2 Step 2: Evaluate inside the parentheses. 4 + 6 = 10 So now we have: 9 × 10 ÷ 2 Step 3: Multiplication and division from left to right. First: 9 × 10 = 90 Then: 90 ÷ 2 = 45 Final Answer: 45

6. Which question is statistical: 'How many books did Noah read last month?' or 'How many books do 7th graders read each month?' Explain why. Answer: 'How many books do 7th graders read each month?' is statistical because it anticipates variability in the number of books read by different students. Solution: Identify the first question: 'How many books did Noah read last month?' This asks about one specific person (Noah) and one specific time (last month). This is a non-statistical question. Identify the second question: 'How many books do 7th graders read each month?' This asks about a group (7th…
   Full step-by-step solution

   Step 1: Identify the first question: 'How many books did Noah read last month?' This asks about one specific person (Noah) and one specific time (last month). The answer is a single number that does not vary. This is a non-statistical question. Step 2: Identify the second question: 'How many books do 7th graders read each month?' This asks about a group (7th graders) and expects different answers from different students. Some might read 0 books, some 2, some 5, etc. The answers will vary. This is a statistical question. Step 3: Conclusion: The second question is statistical because it anticipates variability in the responses.

7. A rectangular prism is drawn with a length of 12 cm, width of 8 cm, and height of 5 cm. If you were to paint all the outside surfaces of this prism, what total surface area would you cover in square centimeters? Answer: 392 Solution: Identify the dimensions: length = 12 cm, width = 8 cm, height = 5 cm Calculate area of front and back faces: 2 × (length × height) = 2 × (12 × 5) = 2 × 60 = 120 cm² Calculate area of left and right faces: 2 × (width × height) = 2 × (8 × 5) = 2 × 40 = 80 cm² Calculate area of top and bottom…
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 12 cm, width = 8 cm, height = 5 cm Step 2: Calculate area of front and back faces: 2 × (length × height) = 2 × (12 × 5) = 2 × 60 = 120 cm² Step 3: Calculate area of left and right faces: 2 × (width × height) = 2 × (8 × 5) = 2 × 40 = 80 cm² Step 4: Calculate area of top and bottom faces: 2 × (length × width) = 2 × (12 × 8) = 2 × 96 = 192 cm² Step 5: Add all areas: 120 + 80 + 192 = 392 cm² The total surface area is 392 square centimeters.