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Relative Frequencies

Grade 8 · Statistics · Worksheet 2

  1. Emma surveyed 175 students about whether they prefer reading fiction or non-fiction. The results are shown in the two-way table below. Calculate the relative frequency of preferring fiction among students who are in Grade 8. Then determine if there is an association between grade level and preference for fiction. | | Fiction | Non-Fiction | Total | |------------|---------|-------------|-------| | Grade 7 | 45 | 35 | 80 | | Grade 8 | 55 | 40 | 95 | | Total | 100 | 75 | 175 | What is the relative frequency of preferring fiction among Grade 8 students? Does this suggest an association between grade level and preference for fiction? Answer: ______________
  2. A cylindrical water tank has a diameter of 12 feet and a height of 20 feet. The tank is filled to 80% of its capacity. What is the volume of water in the tank, in cubic feet? (Use π = 3.14)
    Answer: ______________
  3. A survey of 300 students asked about their preferred sport (Basketball or Soccer) and whether they prefer morning or afternoon practice. The two-way table shows: Basketball-Morning: 45, Basketball-Afternoon: 75, Soccer-Morning: 60, Soccer-Afternoon: 120. Calculate the relative frequency of students who prefer morning practice given they prefer Basketball. Do the relative frequencies suggest an association between sport preference and practice time preference? Answer: ______________
  4. A survey asked 75 students if they prefer reading fiction or non-fiction. The results are shown in the table. Calculate the relative frequency of preferring fiction among students who are in Grade 8. Then, determine if there is an association between grade level and preference. | Grade | Fiction | Non-Fiction | Total | |-------|---------|-------------|-------| | 7 | 15 | 25 | 40 | | 8 | 21 | 14 | 35 | | Total | 36 | 39 | 75 | Answer: ______________
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Answer Key & Explanations

Relative Frequencies · Grade 8 · Worksheet 2

  1. Emma surveyed 175 students about whether they prefer reading fiction or non-fiction. The results are shown in the two-way table below. Calculate the relative frequency of preferring fiction among students who are in Grade 8. Then determine if there is an association between grade level and preference for fiction. | | Fiction | Non-Fiction | Total | |------------|---------|-------------|-------| | Grade 7 | 45 | 35 | 80 | | Grade 8 | 55 | 40 | 95 | | Total | 100 | 75 | 175 | What is the relative frequency of preferring fiction among Grade 8 students? Does this suggest an association between grade level and preference for fiction? Answer: 0.579 (or 57.9%) and yes, there is an association. Solution: Find the number of Grade 8 students who prefer fiction: 55. Find the total number of Grade 8 students: 95. Calculate the relative frequency: 55 ÷ 95 = 0.5789...
    Full step-by-step solution

    Step 1: Find the number of Grade 8 students who prefer fiction: 55. Step 2: Find the total number of Grade 8 students: 95. Step 3: Calculate the relative frequency: 55 ÷ 95 = 0.5789... ≈ 0.579 (or 57.9%). Step 4: Find the overall relative frequency of fiction: 100 ÷ 175 ≈ 0.571 (or 57.1%). Step 5: Compare: 57.9% (Grade 8) vs. 57.1% (overall). The difference is small (0.8 percentage points). However, to check association, also consider Grade 7: 45 ÷ 80 = 0.5625 (56.25%). Since the percentages differ between grades (56.25% for Grade 7, 57.9% for Grade 8), there is a slight association, meaning grade level and preference are not completely independent. The answer is 0.579 (or 57.9%) and yes, there is an association.

  2. A cylindrical water tank has a diameter of 12 feet and a height of 20 feet. The tank is filled to 80% of its capacity. What is the volume of water in the tank, in cubic feet? (Use π = 3.14) Answer: 1808.64 Solution: Find the radius of the cylinder. Radius = diameter ÷ 2 = 12 ÷ 2 = 6 feet. Calculate the full volume of the cylinder.
    Full step-by-step solution

    Step 1: Find the radius of the cylinder. Radius = diameter ÷ 2 = 12 ÷ 2 = 6 feet. Step 2: Calculate the full volume of the cylinder. Volume = π × radius² × height = 3.14 × 6² × 20 = 3.14 × 36 × 20 = 3.14 × 720 = 2260.8 cubic feet. Step 3: Calculate 80% of the full volume. Water volume = 2260.8 × 0.80 = 1808.64 cubic feet. The volume of water in the tank is 1808.64 cubic feet.

  3. A survey of 300 students asked about their preferred sport (Basketball or Soccer) and whether they prefer morning or afternoon practice. The two-way table shows: Basketball-Morning: 45, Basketball-Afternoon: 75, Soccer-Morning: 60, Soccer-Afternoon: 120. Calculate the relative frequency of students who prefer morning practice given they prefer Basketball. Do the relative frequencies suggest an association between sport preference and practice time preference? Answer: 0.375; Yes, there is an association. Solution: Find the total number of students who prefer Basketball: 45 + 75 = 120. Among those who prefer Basketball, the number who prefer morning practice is 45. Conditional relative frequency = 45 / 120 = 0.375 (or 37.5%).
    Full step-by-step solution

    Step 1: Find the total number of students who prefer Basketball: 45 + 75 = 120. Step 2: Among those who prefer Basketball, the number who prefer morning practice is 45. Step 3: Conditional relative frequency = 45 / 120 = 0.375 (or 37.5%). Step 4: Now find the conditional relative frequency for Soccer: total Soccer = 60 + 120 = 180. Morning practice given Soccer = 60 / 180 = 0.333 (or 33.3%). Step 5: Compare 0.375 and 0.333. They are different, so there is an association between sport preference and practice time preference. The answer is 0.375; Yes, there is an association.

  4. A survey asked 75 students if they prefer reading fiction or non-fiction. The results are shown in the table. Calculate the relative frequency of preferring fiction among students who are in Grade 8. Then, determine if there is an association between grade level and preference. | Grade | Fiction | Non-Fiction | Total | |-------|---------|-------------|-------| | 7 | 15 | 25 | 40 | | 8 | 21 | 14 | 35 | | Total | 36 | 39 | 75 | Answer: 0.6; Yes, there is an association Solution: Find the number of Grade 8 students who prefer fiction: 21. Find the total number of Grade 8 students: 35. Calculate the relative frequency: 21 / 35 = 3/5 = 0.6.
    Full step-by-step solution

    Step 1: Find the number of Grade 8 students who prefer fiction: 21. Step 2: Find the total number of Grade 8 students: 35. Step 3: Calculate the relative frequency: 21 / 35 = 3/5 = 0.6. Step 4: Find the overall relative frequency of fiction: 36 / 75 = 12/25 = 0.48. Step 5: Compare: 0.6 is greater than 0.48, so Grade 8 students are more likely to prefer fiction than the overall group. This suggests an association between grade level and preference. The answer is 0.6; Yes, there is an association.