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Statistical Questions · Grade 6 · Worksheet 2

1. Which of the following is a statistical question: 'How many pages are in the book Emma is reading?' or 'How many pages are in the books that Olivia's classmates are reading?' Explain your reasoning. Answer: The second question is statistical because it anticipates variability in the number of pages in different books. Solution: Analyze the first question: 'How many pages are in the book Emma is reading?' This question asks about one specific book. There is only one correct answer, and it does not change. This is a non-statistical question.
   Full step-by-step solution

   Step 1: Analyze the first question: 'How many pages are in the book Emma is reading?' This question asks about one specific book. There is only one correct answer, and it does not change. This is a non-statistical question. Step 2: Analyze the second question: 'How many pages are in the books that Olivia's classmates are reading?' This question asks about a group of people (Olivia's classmates). Each classmate is likely reading a different book, and those books will have different numbers of pages. The answers will vary. This is a statistical question. Step 3: Conclusion: The second question is statistical because it anticipates variability in the responses. The first question is not statistical because it asks for a single, fixed fact.

2. Liam is conducting a survey about favorite school subjects among sixth graders. He surveyed 120 students and found that 30% preferred math, 25% preferred science, 20% preferred English, and the rest preferred art. How many students preferred art? Answer: 30 Solution: First, find the total percentage of students who preferred math, science, and English. Math: 30% Science: 25% English: 20% 30 + 25 + 20 = 75% This means 75% of the students preferred one of these three subjects.
   Full step-by-step solution

   First, find the total percentage of students who preferred math, science, and English. Math: 30% Science: 25% English: 20% Add them: 30 + 25 + 20 = 75% This means 75% of the students preferred one of these three subjects. The rest preferred art, so the percentage for art is: 100% - 75% = 25% Now, calculate how many students that is out of 120 surveyed. 25% of 120 = (25/100) × 120 Simplify: 25/100 = 1/4 (1/4) × 120 = 120/4 = 30 So, 30 students preferred art.

3. Which question is statistical: 'How many books does Mere read each month?' or 'How many books did Mere read last month?' Explain why. Answer: 'How many books does Mere read each month?' is statistical because it anticipates variability in the number of books read from month to month. Solution: Step 2: Analyze the first question: 'How many books does Mere read each month?' This question implies that the number of books Mere reads could change from month to month.
   Full step-by-step solution

   Step 1: Understand the definition of a statistical question: A statistical question anticipates variability in the data that would be collected to answer it. Step 2: Analyze the first question: 'How many books does Mere read each month?' This question implies that the number of books Mere reads could change from month to month. Some months she might read 2 books, other months 5, etc. So the answer would vary, making it a statistical question. Step 3: Analyze the second question: 'How many books did Mere read last month?' This question asks for a specific, fixed number for one particular month. There is only one correct answer (e.g., 4 books). There is no variability in the answer. Step 4: Conclude that the first question is statistical because it anticipates variability, while the second is not. The answer is: 'How many books does Mere read each month?' is statistical.

4. (-6)² - 4 × (21 ÷ 3) + √121 = ? Answer: 19 Solution: Calculate the exponent: (-6)² = 36 Calculate inside parentheses: 21 ÷ 3 = 7 Multiply: 4 × 7 = 28 Calculate the square root: √121 = 11 Combine all parts: 36 - 28 + 11 Subtract: 36 - 28 = 8 Add: 8 + 11 = 19 The answer is 19.
   Full step-by-step solution

   Step 1: Calculate the exponent: (-6)² = 36 Step 2: Calculate inside parentheses: 21 ÷ 3 = 7 Step 3: Multiply: 4 × 7 = 28 Step 4: Calculate the square root: √121 = 11 Step 5: Combine all parts: 36 - 28 + 11 Step 6: Subtract: 36 - 28 = 8 Step 7: Add: 8 + 11 = 19 The answer is 19.

5. A rectangular prism is drawn with dimensions: length = 12 cm, width = 8 cm, and height = 15 cm. If you were to calculate the volume of this prism, what would be the result in cubic centimeters? Answer: 1440 Solution: Identify the formula for the volume of a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 12 cm × 8 cm × 15 cm Multiply the first two numbers: 12 × 8 = 96 Multiply the result by the third number: 96 × 15 = 1440 Include the units: 1440 cubic centimeters…
   Full step-by-step solution

   Step 1: Identify the formula for the volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given values: Volume = 12 cm × 8 cm × 15 cm Step 3: Multiply the first two numbers: 12 × 8 = 96 Step 4: Multiply the result by the third number: 96 × 15 = 1440 Step 5: Include the units: 1440 cubic centimeters The volume of the rectangular prism is 1440 cubic centimeters.

6. Which question is statistical: 'How many books does Emma read in a month?' or 'How many books does Emma read in 2025?' Explain why. Answer: 'How many books does Emma read in a month?' is statistical because the number can vary each month. Solution: Identify the two questions. Question 1: 'How many books does Emma read in a month?' Question 2: 'How many books does Emma read in 2025?' Consider variability.
   Full step-by-step solution

   Step 1: Identify the two questions. Question 1: 'How many books does Emma read in a month?' Question 2: 'How many books does Emma read in 2025?' Step 2: Consider variability. For Question 1, the number of books Emma reads can change from month to month (e.g., 2 books in January, 5 in February, 0 in March). This shows variability, so it is a statistical question. Step 3: For Question 2, the year 2025 is a fixed time period. The number of books Emma reads in that specific year is a single, fixed number (once the year is over). There is no variability in the answer because it refers to one specific time frame. So it is not a statistical question. Step 4: Conclusion: 'How many books does Emma read in a month?' is the statistical question because the answer can vary from month to month.

7. Which of the following is a statistical question? A: 'How many books did Hana read last month?' B: 'How many books did each student in Grade 6 read last month?' Explain why. Answer: Question B is statistical because it anticipates variability in the number of books read by different students. Solution: Step 2: Analyze Question A: 'How many books did Hana read last month?' This asks about one specific person, Hana. There is no variability. So, it is not a statistical question.
   Full step-by-step solution

   Step 1: Understand the definition of a statistical question: It anticipates variability in the data and expects different answers from different individuals. Step 2: Analyze Question A: 'How many books did Hana read last month?' This asks about one specific person, Hana. The answer is a single number (e.g., 3 books). There is no variability. So, it is not a statistical question. Step 3: Analyze Question B: 'How many books did each student in Grade 6 read last month?' This asks about every student in Grade 6. Different students likely read different numbers of books (e.g., 0, 2, 5, 10). The answer will be a set of varying numbers. This anticipates variability. So, it is a statistical question. Step 4: Conclusion: Question B is the statistical question because it expects a range of answers from a group, not a single value.

8. A circular swimming pool is drawn on a coordinate plane with its center at (0, 0) and a point on its circumference at (8, 0). If each unit on the coordinate plane represents 5 feet, what is the actual area of the pool in square feet? (Use π = 3.14) Answer: 5024 Solution: The point (8, 0) is on the circumference, so the radius is 8 units. Each unit represents 5 feet, so the actual radius is 8 × 5 = 40 feet. The area of a circle is π × radius².
   Full step-by-step solution

   Step 1: The point (8, 0) is on the circumference, so the radius is 8 units. Step 2: Each unit represents 5 feet, so the actual radius is 8 × 5 = 40 feet. Step 3: The area of a circle is π × radius². Step 4: Calculate the area: 3.14 × (40)² = 3.14 × 1600 = 5024 square feet. The actual area of the pool is 5024 square feet.

9. A rectangular prism is drawn with dimensions: length = 12 cm, width = 8 cm, and height = 5 cm. If you were to calculate the volume of this prism, what would it be in cubic centimeters? Answer: 480 Solution: The formula for volume of a rectangular prism is length × width × height Substitute the given values: 12 cm × 8 cm × 5 cm First multiply 12 × 8 = 96 Then multiply 96 × 5 = 480 The volume is 480 cubic centimeters
   Full step-by-step solution

   Step 1: The formula for volume of a rectangular prism is length × width × height Step 2: Substitute the given values: 12 cm × 8 cm × 5 cm Step 3: First multiply 12 × 8 = 96 Step 4: Then multiply 96 × 5 = 480 Step 5: The volume is 480 cubic centimeters