Frequency Tables

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Frequency Tables · Grade 8 · Worksheet 2

1. Mason surveyed 127 students at his school about their favorite lunch option and whether they are in 7th grade or 8th grade. The results are shown in the two-way frequency table below: | | Pizza | Tacos | Burgers | Total | |------------|-------|-------|---------|-------| | 7th Grade | 22 | 17 | 27 | 66 | | 8th Grade | 32 | 12 | 17 | 61 | | Total | 54 | 29 | 44 | 127 | What percentage of 8th grade students prefer Pizza as their favorite lunch option? Round your answer to the nearest whole percent. Answer: 52 Solution: Identify the relevant subgroup. The problem asks about 8th grade students. From the table, the total number of 8th grade students is 61.
   Full step-by-step solution

   Step 1: Identify the relevant subgroup. The problem asks about 8th grade students. From the table, the total number of 8th grade students is 61. Step 2: Among 8th graders, the number who prefer Pizza is 32. Step 3: Calculate the fraction: 32/61. Step 4: Convert to a decimal: 32 ÷ 61 ≈ 0.52459. Step 5: Convert to a percentage by multiplying by 100: 0.52459 × 100 = 52.459%. Step 6: Round to the nearest whole percent: 52%. The answer is 52.

2. (2x + 3)(x - 4) - (x² - 5x + 2) = ? Answer: x² - 10 Solution: Expand (2x + 3)(x - 4) 2x * x = 2x² 2x * (-4) = -8x 3 * x = 3x 3 * (-4) = -12 So (2x + 3)(x - 4) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12 Subtract (x² - 5x + 2) (2x² - 5x - 12) - (x² - 5x + 2) = 2x² - 5x - 12 - x² + 5x - 2 2x² - x² = x² -5x + 5x = 0 -12 - 2 = -14 x² + 0 - 14 = x² - 14 The answer is…
   Full step-by-step solution

   Step 1: Expand (2x + 3)(x - 4) 2x * x = 2x² 2x * (-4) = -8x 3 * x = 3x 3 * (-4) = -12 So (2x + 3)(x - 4) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12 Step 2: Subtract (x² - 5x + 2) (2x² - 5x - 12) - (x² - 5x + 2) = 2x² - 5x - 12 - x² + 5x - 2 Step 3: Combine like terms 2x² - x² = x² -5x + 5x = 0 -12 - 2 = -14 Step 4: Final result x² + 0 - 14 = x² - 14 The answer is x² - 14.

3. A school surveyed 200 students about their favorite after-school activity: sports, music, or art. The results are shown in the two-way frequency table below. How many more boys than girls prefer sports? | | Boys | Girls | Total | |------------|------|-------|-------| | Sports | 45 | 25 | 70 | | Music | 20 | 40 | 60 | | Art | 15 | 35 | 50 | | Total | 80 | 120 | 200 | Answer: 20 Solution: Identify the relevant data from the table. We are told to find how many more boys than girls prefer sports. - Boys who prefer sports = 45 - Girls who prefer sports = 25 Subtract the number of girls from the number of boys.
   Full step-by-step solution

   Step 1: Identify the relevant data from the table. We are told to find how many more boys than girls prefer sports. From the row labeled "Sports": - Boys who prefer sports = 45 - Girls who prefer sports = 25 Step 2: Subtract the number of girls from the number of boys. Difference = Boys (sports) − Girls (sports) Difference = 45 − 25 Step 3: Calculate the result. 45 − 25 = 20 Step 4: Interpret the result. This means 20 more boys than girls prefer sports. Final answer: 20

4. 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.

5. (3x² - 2x + 7) - (x² + 4x - 5) = ? Answer: 2x² - 6x + 12 Solution: Write the expression: (3x² - 2x + 7) - (x² + 4x - 5) Distribute the negative sign: 3x² - 2x + 7 - x² - 4x + 5 Combine x² terms: 3x² - x² = 2x² Combine x terms: -2x - 4x = -6x Combine constant terms: 7 + 5 = 12 Write the final expression: 2x² - 6x + 12 The answer is 2x² - 6x + 12.
   Full step-by-step solution

   Step 1: Write the expression: (3x² - 2x + 7) - (x² + 4x - 5) Step 2: Distribute the negative sign: 3x² - 2x + 7 - x² - 4x + 5 Step 3: Combine x² terms: 3x² - x² = 2x² Step 4: Combine x terms: -2x - 4x = -6x Step 5: Combine constant terms: 7 + 5 = 12 Step 6: Write the final expression: 2x² - 6x + 12 The answer is 2x² - 6x + 12.

6. A community center surveyed 180 teenagers about their preferred method of communication and whether they own a smartphone. The results are shown in the two-way frequency table below: | | Text Messaging | Social Media | Phone Calls | Total | |-----------------|----------------|--------------|-------------|-------| | Smartphone | 48 | 36 | 12 | 96 | | No Smartphone | 24 | 42 | 18 | 84 | | Total | 72 | 78 | 30 | 180 | What percentage of teenagers who own a smartphone prefer text messaging as their primary communication method? Round your answer to the nearest whole percent. Answer: 50 Solution: Identify the relevant subgroup - teenagers who own a smartphone. The total number of smartphone owners is 96. Within this subgroup, identify those who prefer text messaging.
   Full step-by-step solution

   Step 1: Identify the relevant subgroup - teenagers who own a smartphone. The total number of smartphone owners is 96. Step 2: Within this subgroup, identify those who prefer text messaging. According to the table, 48 smartphone owners prefer text messaging. Step 3: Calculate the fraction: 48/96 = 0.5 Step 4: Convert to percentage: 0.5 × 100 = 50% Step 5: Since the result is already a whole number, no rounding is needed. The answer is 50%.