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Statistical Questions

Grade 6 · Statistics · Worksheet 1

  1. Which of these is a statistical question: 'How many books does Kaia read in a year?' or 'How many books do students in Grade 6 read in a year?' Explain why. Answer: ______________
  2. Liam is conducting a survey about favorite school subjects among sixth graders. He surveyed 120 students and found that 40% preferred math, 25% preferred science, and the rest preferred language arts. How many students preferred language arts? Answer: ______________
  3. 3² × (12 - 8) ÷ 2 = ? Answer: ______________
  4. Which question is statistical: 'How many minutes does Emma spend on homework each day?' or 'How many minutes did Olivia spend on homework yesterday?' Explain why. Answer: ______________
  5. A school is organizing a field trip to the science museum. The total cost for the trip is $1,800, which includes bus rental and admission fees for all students. 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: ______________
  6. Liam is conducting a survey about favorite school subjects among 6th graders. He surveyed 120 students and found that 40% preferred math, 25% preferred science, and the rest preferred language arts. How many students preferred language arts? Answer: ______________
  7. 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: ______________
  8. A survey asked 1250 middle school students about their favorite type of book. The results showed that 28% preferred fantasy, 32% preferred mystery, 18% preferred science fiction, and the rest preferred historical fiction. How many students preferred historical fiction? Answer: ______________
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Answer Key & Explanations

Statistical Questions · Grade 6 · Worksheet 1

  1. Which of these is a statistical question: 'How many books does Kaia read in a year?' or 'How many books do students in Grade 6 read in a year?' Explain why. Answer: The second question is statistical because it anticipates variability in the number of books read by different students. Solution: Identify the first question: 'How many books does Kaia read in a year?' This asks about one specific person, Kaia, so it will have only one answer. There is no variability. Step 2: Identify the second question: 'How many books do students in Grade 6 read in a year?' This asks about a group of…
    Full step-by-step solution

    Step 1: Identify the first question: 'How many books does Kaia read in a year?' This asks about one specific person, Kaia, so it will have only one answer. There is no variability. Step 2: Identify the second question: 'How many books do students in Grade 6 read in a year?' This asks about a group of students, and different students likely read different numbers of books. The answers will vary. Step 3: A statistical question is one that anticipates variability in the data. Since the second question expects a range of different answers, it is statistical. The first question is not statistical. The answer is: The second question is statistical.

  2. Liam is conducting a survey about favorite school subjects among sixth graders. He surveyed 120 students and found that 40% preferred math, 25% preferred science, and the rest preferred language arts. How many students preferred language arts? Answer: 42 Solution: Find the total percentage of students who preferred math and science. Math: 40% Science: 25% Total percentage for math and science = 40% + 25% = 65% Find the percentage of students who preferred language arts.
    Full step-by-step solution

    Step 1: Find the total percentage of students who preferred math and science. Math: 40% Science: 25% Total percentage for math and science = 40% + 25% = 65% Step 2: Find the percentage of students who preferred language arts. Since the rest preferred language arts, subtract the total percentage for math and science from 100%. Language arts percentage = 100% - 65% = 35% Step 3: Calculate the number of students who preferred language arts. Total students surveyed = 120 Number who preferred language arts = 35% of 120 35% of 120 = (35/100) × 120 First, simplify: 35/100 = 7/20 Then, (7/20) × 120 = 7 × (120/20) = 7 × 6 = 42 Step 4: State the final answer. Therefore, 42 students preferred language arts.

  3. 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.

  4. Which question is statistical: 'How many minutes does Emma spend on homework each day?' or 'How many minutes did Olivia spend on homework yesterday?' Explain why. Answer: 'How many minutes does Emma spend on homework each day?' is statistical because it anticipates variability in the number of minutes from day to day. 'How many minutes did Olivia spend on homework yesterday?' is not statistical because it asks about a single, fixed event with no variability. Solution: A statistical question is one that anticipates variability in the data related to the question. This means the answer is not a single, fixed number but can change based on different circumstances or individuals. Since Emma might spend 30 minutes one day, 45 minutes another day, and 20 minutes on…
    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. This means the answer is not a single, fixed number but can change based on different circumstances or individuals. Step 2: Analyze the first question: 'How many minutes does Emma spend on homework each day?' This question asks about the amount of time Emma spends on homework on different days. Since Emma might spend 30 minutes one day, 45 minutes another day, and 20 minutes on a third day, the answer varies from day to day. Therefore, this question anticipates variability and is statistical. Step 3: Analyze the second question: 'How many minutes did Olivia spend on homework yesterday?' This question asks about a specific event (yesterday) and a specific person (Olivia). The answer is a single, fixed number (e.g., 40 minutes). There is no variability because it refers to one particular day. Therefore, this question is not statistical. Step 4: Conclusion: The first question is statistical because it expects different answers each day. The second question is not statistical because it asks for a single, fixed value. The answer is: 'How many minutes does Emma spend on homework each day?' is statistical.

  5. A school is organizing a field trip to the science museum. The total cost for the trip is $1,800, which includes bus rental and admission fees for all students. 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: 25 Solution: Find the remaining cost after the fundraiser. Total cost = $1,800 Money already raised = $675 Remaining cost = $1,800 - $675 = $1,125 Divide the remaining cost equally among all students to find the cost per student.
    Full step-by-step solution

    Step 1: Find the remaining cost after the fundraiser. Total cost = $1,800 Money already raised = $675 Remaining cost = $1,800 - $675 = $1,125 Step 2: Divide the remaining cost equally among all students to find the cost per student. Number of students = 45 Cost per student = $1,125 ÷ 45 Step 3: Perform the division. $1,125 ÷ 45 = $25 Each student needs to pay $25.

  6. Liam is conducting a survey about favorite school subjects among 6th graders. He surveyed 120 students and found that 40% preferred math, 25% preferred science, and the rest preferred language arts. How many students preferred language arts? Answer: 42 Solution: We know 120 students were surveyed. 40% preferred math, 25% preferred science, and the rest preferred language arts. We need to find the number of students who preferred language arts.
    Full step-by-step solution

    Step 1: Understand the problem. We know 120 students were surveyed. 40% preferred math, 25% preferred science, and the rest preferred language arts. We need to find the number of students who preferred language arts. Step 2: Find the total percentage for math and science. Math: 40% Science: 25% Total percentage for math and science = 40% + 25% = 65% Step 3: Find the percentage for language arts. Since all students must add up to 100%, Language arts percentage = 100% − 65% = 35% Step 4: Calculate the number of students who preferred language arts. 35% of 120 students = (35/100) × 120 First, 35/100 = 0.35 Then, 0.35 × 120 = 42 Step 5: Conclusion. The number of students who preferred language arts is 42.

  7. 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.

  8. A survey asked 1250 middle school students about their favorite type of book. The results showed that 28% preferred fantasy, 32% preferred mystery, 18% preferred science fiction, and the rest preferred historical fiction. How many students preferred historical fiction? Answer: 275 Solution: We know the total number of students is 1250. Fantasy: 28% Mystery: 32% Science Fiction: 18% Find the total percentage of the first three types. 28% + 32% + 18% = 78% Find the percentage for historical fiction.
    Full step-by-step solution

    Let's solve this step-by-step. Step 1: Understand the problem. We know the total number of students is 1250. The percentages for favorite book types are: Fantasy: 28% Mystery: 32% Science Fiction: 18% Historical Fiction: the rest Step 2: Find the total percentage of the first three types. 28% + 32% + 18% = 78% Step 3: Find the percentage for historical fiction. Since all students must add up to 100%, Historical Fiction = 100% - 78% = 22% Step 4: Calculate the number of students who preferred historical fiction. 22% of 1250 = (22/100) * 1250 Step 5: Perform the calculation. First, 22/100 = 0.22 Then, 0.22 * 1250 = 275 Step 6: Conclusion. So, the number of students who preferred historical fiction is 275.