Frequency Tables

lessonbunny.com

Answer Key & Explanations

Frequency Tables · Grade 8 · Worksheet 3

1. A school surveyed 200 students about their favorite extracurricular activities and whether they play a musical instrument. The results are shown in the two-way frequency table below: | | Sports | Arts | Academic Clubs | Total | |-----------------|--------|------|----------------|-------| | Plays Instrument| 35 | 42 | 18 | 95 | | No Instrument | 45 | 28 | 32 | 105 | | Total | 80 | 70 | 50 | 200 | What percentage of students who play an instrument prefer Arts as their favorite activity? Round your answer to the nearest whole percent. Answer: 44% Solution: We are asked: "What percentage of students who play an instrument prefer Arts as their favorite activity?" Identify the relevant group. The group is "students who play an instrument." From the table, the total number of students who play an instrument is 95.
   Full step-by-step solution

   We are asked: "What percentage of students who play an instrument prefer Arts as their favorite activity?" Step 1: Identify the relevant group. The group is "students who play an instrument." From the table, the total number of students who play an instrument is 95. Step 2: From that group, find how many prefer Arts. From the row "Plays Instrument" and column "Arts", the number is 42. Step 3: The percentage is (part / whole) × 100. So, percentage = (42 / 95) × 100. Step 4: Calculate 42 divided by 95. 42 ÷ 95 ≈ 0.442105... Step 5: Multiply by 100 to get percent. 0.442105 × 100 ≈ 44.2105%. Step 6: Round to the nearest whole percent. 44.2105% rounds to 44%. Final answer: 44%

2. Emma surveyed 150 students at her school about their favorite type of book and whether they are in 7th grade or 8th grade. The results are shown in the two-way frequency table below: | | Fiction | Nonfiction | Mystery | Total | |------------|---------|------------|---------|-------| | 7th Grade | 35 | 20 | 25 | 80 | | 8th Grade | 30 | 15 | 25 | 70 | | Total | 65 | 35 | 50 | 150 | What percentage of 8th grade students prefer Mystery books? Round your answer to the nearest whole percent. Answer: 36 Solution: Identify the relevant group. We are looking at 8th grade students. From the table, the total number of 8th graders is 70.
   Full step-by-step solution

   Step 1: Identify the relevant group. We are looking at 8th grade students. From the table, the total number of 8th graders is 70. Step 2: Among 8th graders, the number who prefer Mystery is 25. Step 3: Calculate the fraction: 25 divided by 70 = 0.3571... Step 4: Convert to a percentage by multiplying by 100: 0.3571 x 100 = 35.71% Step 5: Round to the nearest whole percent: 36%. The answer is 36.

3. 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.

4. A two-way frequency table shows the transportation preferences of 150 middle school students, categorized by grade level (7th or 8th). The rows represent grade levels and the columns represent transportation methods: Bus, Bike, and Walk. There are 60 eighth graders total. The number of seventh graders who prefer the bus is 25. The number of students who prefer biking is 40, and 15 of them are eighth graders. If the total number of students who prefer walking is 50, and 20 of the walkers are seventh graders, how many seventh graders prefer the bus? Answer: 25 Solution: Find the total number of seventh graders. Total students = 150 Total eighth graders = 60 So, total seventh graders = 150 - 60 = 90 Analyze the walking column.
   Full step-by-step solution

   Step 1: Find the total number of seventh graders. Total students = 150 Total eighth graders = 60 So, total seventh graders = 150 - 60 = 90 Step 2: Analyze the walking column. Total who prefer walking = 50 Seventh graders who walk = 20 So, eighth graders who walk = 50 - 20 = 30 Step 3: Analyze the biking column. Total who prefer biking = 40 Eighth graders who bike = 15 So, seventh graders who bike = 40 - 15 = 25 Step 4: Find seventh graders who prefer the bus. Total seventh graders = 90 Seventh graders who bike = 25 Seventh graders who walk = 20 So, seventh graders who prefer the bus = 90 - 25 - 20 = 25 The answer is 25.

5. √(64) + 4³ - 5² = ? Answer: 47 Solution: Evaluate the square root: √(64) = 8 Evaluate the exponent: 4³ = 4 × 4 × 4 = 64 Evaluate the other exponent: 5² = 25 Substitute back into the expression: 8 + 64 - 25 Perform addition first: 8 + 64 = 72 Perform subtraction: 72 - 25 = 47 The answer is 47.
   Full step-by-step solution

   Step 1: Evaluate the square root: √(64) = 8 Step 2: Evaluate the exponent: 4³ = 4 × 4 × 4 = 64 Step 3: Evaluate the other exponent: 5² = 25 Step 4: Substitute back into the expression: 8 + 64 - 25 Step 5: Perform addition first: 8 + 64 = 72 Step 6: Perform subtraction: 72 - 25 = 47 The answer is 47.