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Statistical Questions

Grade 6 · Statistics · Worksheet 2

  1. (-3)² + 4 × (15 ÷ 5) - √36 = ? Answer: ______________
  2. A middle school is planning a field trip to the science museum. The total cost for the trip is $1,875, which includes bus rental and admission fees. If 45 students are going on the trip, and the school has already raised $675 through a fundraiser, how much does each student need to pay to cover the remaining cost? Answer: ______________
  3. A school is planning a field trip to the science museum. The total cost for the trip is $1,250, which includes bus rental and admission fees. If 32 students are going on the trip, and the school has already raised $350 through a bake sale, how much does each student need to pay to cover the remaining cost? Answer: ______________
  4. Emma is conducting a survey about favorite types of movies among sixth graders. She surveyed 240 students and found that 35% preferred action movies, 30% preferred comedy movies, and the rest preferred animated movies. How many students preferred animated movies? Answer: ______________
  5. 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: ______________
  6. A rectangular prism is drawn with dimensions: length = 12 cm, width = 8 cm, and height = 5 cm. If you calculate the volume of this prism, what is your result in cubic centimeters? Answer: ______________
  7. Emma is looking at a bar graph that shows the number of books read by each student in her class last month. The graph has bars for 20 students. Some bars are tall, some are short. She wonders if she can ask a question about the data that will have variability in the answers. Which of the following two questions is a statistical question: 'How many books did Emma read last month?' or 'How many books did the students in Emma's class read last month?' Explain your reasoning. Answer: ______________
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Answer Key & Explanations

Statistical Questions · Grade 6 · Worksheet 2

  1. (-3)² + 4 × (15 ÷ 5) - √36 = ? Answer: 15 Solution: Calculate inside parentheses: 15 ÷ 5 = 3 Calculate exponents: (-3)² = 9 Calculate multiplication: 4 × 3 = 12 Calculate square root: √36 = 6 Combine all parts: 9 + 12 - 6 Add and subtract left to right: 9 + 12 = 21, then 21 - 6 = 15 The answer is 15.
    Full step-by-step solution

    Step 1: Calculate inside parentheses: 15 ÷ 5 = 3 Step 2: Calculate exponents: (-3)² = 9 Step 3: Calculate multiplication: 4 × 3 = 12 Step 4: Calculate square root: √36 = 6 Step 5: Combine all parts: 9 + 12 - 6 Step 6: Add and subtract left to right: 9 + 12 = 21, then 21 - 6 = 15 The answer is 15.

  2. A middle school is planning a field trip to the science museum. The total cost for the trip is $1,875, which includes bus rental and admission fees. If 45 students are going on the trip, and the school has already raised $675 through a fundraiser, how much does each student need to pay to cover the remaining cost? Answer: 26.67 Solution: Calculate the remaining cost after the fundraiser. Total cost: $1,875 Amount raised: $675 Remaining cost = $1,875 - $675 = $1,200 Divide the remaining cost by the number of students to find the cost per student.
    Full step-by-step solution

    Step 1: Calculate the remaining cost after the fundraiser. Total cost: $1,875 Amount raised: $675 Remaining cost = $1,875 - $675 = $1,200 Step 2: Divide the remaining cost by the number of students to find the cost per student. Number of students: 45 Cost per student = $1,200 ÷ 45 Step 3: Perform the division. $1,200 ÷ 45 = $26.666... Step 4: Round to the nearest cent for a monetary value. $26.666... ≈ $26.67 Each student needs to pay $26.67 to cover the remaining cost.

  3. A school is planning a field trip to the science museum. The total cost for the trip is $1,250, which includes bus rental and admission fees. If 32 students are going on the trip, and the school has already raised $350 through a bake sale, how much does each student need to pay to cover the remaining cost? Answer: 28.125 Solution: Calculate the remaining cost after the bake sale: $1,250 - $350 = $900 Divide the remaining cost by the number of students: $900 ÷ 32 Perform the division: 900 ÷ 32 = 28.125 Each student needs to pay $28.125 to cover the remaining cost.
    Full step-by-step solution

    Step 1: Calculate the remaining cost after the bake sale: $1,250 - $350 = $900 Step 2: Divide the remaining cost by the number of students: $900 ÷ 32 Step 3: Perform the division: 900 ÷ 32 = 28.125 Each student needs to pay $28.125 to cover the remaining cost.

  4. Emma is conducting a survey about favorite types of movies among sixth graders. She surveyed 240 students and found that 35% preferred action movies, 30% preferred comedy movies, and the rest preferred animated movies. How many students preferred animated movies? Answer: 84 Solution: Find the percentage of students who preferred animated movies. Total percentage must equal 100% Action: 35% Comedy: 30% Animated: 100% - 35% - 30% = 35% Calculate the number of students who preferred animated movies.
    Full step-by-step solution

    Step 1: Find the percentage of students who preferred animated movies. Total percentage must equal 100% Action: 35% Comedy: 30% Animated: 100% - 35% - 30% = 35% Step 2: Calculate the number of students who preferred animated movies. Total students: 240 Students preferring animated movies: 35% of 240 35% of 240 = 0.35 × 240 = 84 Step 3: Verify the answer. Action: 35% of 240 = 84 students Comedy: 30% of 240 = 72 students Animated: 35% of 240 = 84 students Total: 84 + 72 + 84 = 240 students ✓ The answer is 84.

  5. 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.

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

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

  7. Emma is looking at a bar graph that shows the number of books read by each student in her class last month. The graph has bars for 20 students. Some bars are tall, some are short. She wonders if she can ask a question about the data that will have variability in the answers. Which of the following two questions is a statistical question: 'How many books did Emma read last month?' or 'How many books did the students in Emma's class read last month?' Explain your reasoning. Answer: 'How many books did the students in Emma's class read last month?' is a statistical question. Solution: Understand what makes a question statistical. A statistical question is one that anticipates variability in the data. Analyze the second question: 'How many books did the students in Emma's class read last month?' This question is about a group of 20 students.
    Full step-by-step solution

    Step 1: Understand what makes a question statistical. A statistical question is one that anticipates variability in the data. This means that if you ask the question to different people, you expect to get different answers. Step 2: Analyze the first question: 'How many books did Emma read last month?' This question is about one specific person (Emma). There is only one answer, and it does not vary. So this is a non-statistical question. Step 3: Analyze the second question: 'How many books did the students in Emma's class read last month?' This question is about a group of 20 students. Different students likely read different numbers of books, so the answers will vary. This anticipates variability. Step 4: Conclude: The question 'How many books did the students in Emma's class read last month?' is a statistical question because it expects a range of answers (e.g., some students read 0 books, some read 5, some read 10, etc.), while the question about Emma alone has only one answer. Final answer: 'How many books did the students in Emma's class read last month?' is a statistical question.