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Frequency Tables

Grade 8 · Statistics · Worksheet 3

  1. Hana surveyed 120 students at her school about their favorite type of music and whether they play a musical instrument. The results are shown in the two-way frequency table below: | | Pop | Rock | Hip-Hop | Total | |-----------------|-----|------|---------|-------| | Plays Instrument | 22 | 18 | 20 | 60 | | Does Not Play | 26 | 14 | 20 | 60 | | Total | 48 | 32 | 40 | 120 | What percentage of students who play a musical instrument prefer Pop music? Round your answer to the nearest whole percent. Answer: ______________
  2. (2x + 3)(x - 4) - (x + 2)(x - 5) = ? Answer: ______________
  3. A survey asked 120 students about their preference for two sports: basketball and soccer. 75 students like basketball, 60 students like soccer, and 25 students like both sports. Complete the two-way frequency table and find how many students like only basketball. Answer: ______________
  4. A community center surveyed 180 teenagers about their preferred method of communication and whether they participate in team sports. The results are shown in the two-way frequency table below: | | Text Messaging | Social Media | Video Calls | Total | |-----------------|----------------|--------------|-------------|-------| | Play Sports | 35 | 28 | 12 | 75 | | No Sports | 25 | 52 | 28 | 105 | | Total | 60 | 80 | 40 | 180 | What percentage of teenagers who play sports prefer text messaging as their communication method? Round your answer to the nearest whole percent. Answer: ______________
  5. A survey asked 150 students about their preference for two activities: reading and gaming. 80 students like reading, 70 students like gaming, and 30 students like both activities. Complete the two-way frequency table and find how many students like only reading. Answer: ______________
  6. A school surveyed 300 students about their favorite type of movie and whether they stream movies regularly. The results showed: 180 students stream movies regularly, 120 do not. Among those who stream regularly, 108 prefer action movies. Among those who do not stream regularly, 45 prefer comedy movies. If the total number of students who prefer action movies is 150, how many students who do not stream regularly prefer action movies? Answer: ______________
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Answer Key & Explanations

Frequency Tables · Grade 8 · Worksheet 3

  1. Hana surveyed 120 students at her school about their favorite type of music and whether they play a musical instrument. The results are shown in the two-way frequency table below: | | Pop | Rock | Hip-Hop | Total | |-----------------|-----|------|---------|-------| | Plays Instrument | 22 | 18 | 20 | 60 | | Does Not Play | 26 | 14 | 20 | 60 | | Total | 48 | 32 | 40 | 120 | What percentage of students who play a musical instrument prefer Pop music? Round your answer to the nearest whole percent. Answer: 37 Solution: Identify the relevant group. We are looking at students who play a musical instrument. From the table, the total number of students who play an instrument is 60.
    Full step-by-step solution

    Step 1: Identify the relevant group. We are looking at students who play a musical instrument. From the table, the total number of students who play an instrument is 60. Step 2: Within that group, the number who prefer Pop music is 22. Step 3: To find the percentage, divide the number who prefer Pop by the total number who play an instrument: 22 / 60 = 0.36666... Step 4: Convert to a percentage by multiplying by 100: 0.36666... * 100 = 36.666...% Step 5: Round to the nearest whole percent: 37%. The answer is 37.

  2. (2x + 3)(x - 4) - (x + 2)(x - 5) = ? Answer: x² - 7x - 2 Solution: Expand (2x + 3)(x - 4) = 2x(x) + 2x(-4) + 3(x) + 3(-4) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12 Expand (x + 2)(x - 5) = x(x) + x(-5) + 2(x) + 2(-5) = x² - 5x + 2x - 10 = x² - 3x - 10 = (2x² - 5x - 12) - (x² - 3x - 10) = 2x² - 5x - 12 - x² + 3x + 10 = (2x² - x²) + (-5x + 3x) + (-12 + 10) = x² - 2x -…
    Full step-by-step solution

    Step 1: Expand (2x + 3)(x - 4) = 2x(x) + 2x(-4) + 3(x) + 3(-4) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12 Step 2: Expand (x + 2)(x - 5) = x(x) + x(-5) + 2(x) + 2(-5) = x² - 5x + 2x - 10 = x² - 3x - 10 Step 3: Subtract the second expression from the first = (2x² - 5x - 12) - (x² - 3x - 10) = 2x² - 5x - 12 - x² + 3x + 10 Step 4: Combine like terms = (2x² - x²) + (-5x + 3x) + (-12 + 10) = x² - 2x - 2 The answer is x² - 2x - 2.

  3. A survey asked 120 students about their preference for two sports: basketball and soccer. 75 students like basketball, 60 students like soccer, and 25 students like both sports. Complete the two-way frequency table and find how many students like only basketball. Answer: 50 Solution: Set up the two-way frequency table with rows for 'Like Basketball' and 'Do Not Like Basketball', and columns for 'Like Soccer' and 'Do Not Like Soccer'. - Total students = 120 - Like basketball = 75 - Like soccer = 60 - Like both = 25 (this goes in the intersection of 'Like Basketball' and 'Like…
    Full step-by-step solution

    Step 1: Set up the two-way frequency table with rows for 'Like Basketball' and 'Do Not Like Basketball', and columns for 'Like Soccer' and 'Do Not Like Soccer'. Step 2: Place the given numbers: - Total students = 120 - Like basketball = 75 - Like soccer = 60 - Like both = 25 (this goes in the intersection of 'Like Basketball' and 'Like Soccer') Step 3: Calculate students who like basketball but not soccer: 75 (total like basketball) - 25 (like both) = 50 Step 4: Calculate students who like soccer but not basketball: 60 (total like soccer) - 25 (like both) = 35 Step 5: Calculate students who like neither sport: 120 (total) - 75 (like basketball) - 35 (like only soccer) = 10 Or: 120 - 60 (like soccer) - 50 (like only basketball) = 10 Step 6: The number of students who like only basketball is 50. The answer is 50.

  4. A community center surveyed 180 teenagers about their preferred method of communication and whether they participate in team sports. The results are shown in the two-way frequency table below: | | Text Messaging | Social Media | Video Calls | Total | |-----------------|----------------|--------------|-------------|-------| | Play Sports | 35 | 28 | 12 | 75 | | No Sports | 25 | 52 | 28 | 105 | | Total | 60 | 80 | 40 | 180 | What percentage of teenagers who play sports prefer text messaging as their communication method? Round your answer to the nearest whole percent. Answer: 47 Solution: Identify the relevant subgroup - teenagers who play sports. The total number of teenagers who play sports is 75. Within this subgroup, identify those who prefer text messaging.
    Full step-by-step solution

    Step 1: Identify the relevant subgroup - teenagers who play sports. The total number of teenagers who play sports is 75. Step 2: Within this subgroup, identify those who prefer text messaging. From the table, 35 teenagers who play sports prefer text messaging. Step 3: Calculate the fraction: 35/75 Step 4: Convert the fraction to a percentage: (35 ÷ 75) × 100 = 0.4666... × 100 = 46.666...% Step 5: Round to the nearest whole percent: 47% The answer is 47.

  5. A survey asked 150 students about their preference for two activities: reading and gaming. 80 students like reading, 70 students like gaming, and 30 students like both activities. Complete the two-way frequency table and find how many students like only reading. Answer: 50 Solution: - Total students: 150 - Students who like reading: 80 - Students who like gaming: 70 - Students who like both activities: 30 Students who like only reading = Total who like reading - Students who like both activities = 80 - 30 = 50 Only reading: 50 Only gaming: 70 - 30 = 40 Both activities: 30…
    Full step-by-step solution

    Step 1: Identify the given information: - Total students: 150 - Students who like reading: 80 - Students who like gaming: 70 - Students who like both activities: 30 Step 2: Calculate students who like only reading: Students who like only reading = Total who like reading - Students who like both activities = 80 - 30 = 50 Step 3: Verify with the two-way table: Only reading: 50 Only gaming: 70 - 30 = 40 Both activities: 30 Neither activity: 150 - (50 + 40 + 30) = 30 Total: 50 + 40 + 30 + 30 = 150 ✓ The answer is 50.

  6. A school surveyed 300 students about their favorite type of movie and whether they stream movies regularly. The results showed: 180 students stream movies regularly, 120 do not. Among those who stream regularly, 108 prefer action movies. Among those who do not stream regularly, 45 prefer comedy movies. If the total number of students who prefer action movies is 150, how many students who do not stream regularly prefer action movies? Answer: 42 Solution: We know the total number of students is 300, with 180 who stream regularly and 120 who do not. Among the 180 who stream regularly, 108 prefer action movies. The total number of students who prefer action movies is 150.
    Full step-by-step solution

    Step 1: We know the total number of students is 300, with 180 who stream regularly and 120 who do not. Step 2: Among the 180 who stream regularly, 108 prefer action movies. Step 3: The total number of students who prefer action movies is 150. Step 4: To find how many students who do not stream regularly prefer action movies, subtract the action movie fans who stream regularly from the total action movie fans: 150 - 108 = 42 Step 5: Verify this makes sense with the other information: Among the 120 who do not stream regularly, if 42 prefer action movies, then the remaining 120 - 42 = 78 prefer other types of movies. This is consistent with the given information that 45 prefer comedy movies among non-streamers. The answer is 42.