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Categorical Data

Grade 11 · Statistics · Worksheet 1

  1. Sophia surveyed 56 students about their preferred type of movie and whether they prefer watching alone or with friends. The results are: 11 prefer Action and Alone, 6 prefer Action and With Friends, 16 prefer Comedy and Alone, 9 prefer Comedy and With Friends, 8 prefer Drama and Alone, and 6 prefer Drama and With Friends. Create a two-way frequency table summarizing this categorical data. Answer: ______________
  2. Ava surveyed 42 students about their favorite subject and extracurricular activity. The results showed: 12 students like Math and Sports, 8 like Math and Arts, 7 like Science and Sports, 9 like Science and Arts, 4 like English and Sports, and 2 like English and Arts. Create a two-way frequency table summarizing this data. Answer: ______________
  3. Kaia surveyed 49 students at her school about their preferred method of physical activity and their year level. The results are as follows: 13 Year 11 students prefer team sports, 7 Year 11 students prefer individual sports, and 5 Year 11 students prefer no activity. For Year 12 students, 9 prefer team sports, 11 prefer individual sports, and 4 prefer no activity. Organize this data into a two-way frequency table summarizing the counts of students by year level and preferred activity type. What is the total number of students who prefer individual sports? Answer: ______________
  4. Kaia surveyed 56 students about their preferred method of learning: 24 prefer visual, 18 prefer auditory, and 14 prefer kinesthetic. Create a frequency table summarizing this categorical data. Answer: ______________
  5. Isabella, a market researcher, surveyed 72 customers at a local farmers' market about their preferred fruit (Apples, Bananas, or Cherries) and whether they shop weekly (Yes or No). The results showed: 22 customers preferred Apples, 17 preferred Bananas, and the rest preferred Cherries. Of those who preferred Apples, 12 shop weekly. Of those who preferred Bananas, 7 shop weekly. Of those who preferred Cherries, 10 shop weekly. Construct a complete two-way frequency table summarizing the data, showing the counts for each combination of fruit preference and weekly shopping habit, along with row totals, column totals, and a grand total. Answer: ______________
  6. Emma surveyed 30 students about their favorite subject: 15 chose Math, 10 chose Science, and 5 chose English. Create a frequency table summarizing this data. Answer: ______________
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Answer Key & Explanations

Categorical Data · Grade 11 · Worksheet 1

  1. Sophia surveyed 56 students about their preferred type of movie and whether they prefer watching alone or with friends. The results are: 11 prefer Action and Alone, 6 prefer Action and With Friends, 16 prefer Comedy and Alone, 9 prefer Comedy and With Friends, 8 prefer Drama and Alone, and 6 prefer Drama and With Friends. Create a two-way frequency table summarizing this categorical data. Answer: 56 Solution: Set up the two-way table structure. Let rows be the movie genre (Action, Comedy, Drama) and columns be the watching preference (Alone, With Friends). - Action and Alone: 11 - Action and With Friends: 6 - Comedy and Alone: 16 - Comedy and With Friends: 9 - Drama and Alone: 8 - Drama and With…
    Full step-by-step solution

    Step 1: Set up the two-way table structure. Let rows be the movie genre (Action, Comedy, Drama) and columns be the watching preference (Alone, With Friends). Step 2: Fill in the given joint frequencies: - Action and Alone: 11 - Action and With Friends: 6 - Comedy and Alone: 16 - Comedy and With Friends: 9 - Drama and Alone: 8 - Drama and With Friends: 6 Step 3: Calculate row totals: - Action total: 11 + 6 = 17 - Comedy total: 16 + 9 = 25 - Drama total: 8 + 6 = 14 Step 4: Calculate column totals: - Alone total: 11 + 16 + 8 = 35 - With Friends total: 6 + 9 + 6 = 21 Step 5: Calculate grand total from row totals: 17 + 25 + 14 = 56 Or from column totals: 35 + 21 = 56 The completed two-way frequency table is: Alone With Friends Total Action 11 6 17 Comedy 16 9 25 Drama 8 6 14 Total 35 21 56 The grand total is 56, which matches the number of students surveyed.

  2. Ava surveyed 42 students about their favorite subject and extracurricular activity. The results showed: 12 students like Math and Sports, 8 like Math and Arts, 7 like Science and Sports, 9 like Science and Arts, 4 like English and Sports, and 2 like English and Arts. Create a two-way frequency table summarizing this data. Answer: 42 Solution: Set up the two-way table structure with Subjects as rows and Activities as columns.
    Full step-by-step solution

    Step 1: Set up the two-way table structure with Subjects as rows and Activities as columns. Step 2: Fill in the given frequencies: - Math & Sports: 12 - Math & Arts: 8 - Science & Sports: 7 - Science & Arts: 9 - English & Sports: 4 - English & Arts: 2 Step 3: Calculate row totals: - Math total: 12 + 8 = 20 - Science total: 7 + 9 = 16 - English total: 4 + 2 = 6 Step 4: Calculate column totals: - Sports total: 12 + 7 + 4 = 23 - Arts total: 8 + 9 + 2 = 19 Step 5: Verify grand total: 20 + 16 + 6 = 42 or 23 + 19 = 42 The completed two-way table shows all frequencies and totals correctly sum to 42 students.

  3. Kaia surveyed 49 students at her school about their preferred method of physical activity and their year level. The results are as follows: 13 Year 11 students prefer team sports, 7 Year 11 students prefer individual sports, and 5 Year 11 students prefer no activity. For Year 12 students, 9 prefer team sports, 11 prefer individual sports, and 4 prefer no activity. Organize this data into a two-way frequency table summarizing the counts of students by year level and preferred activity type. What is the total number of students who prefer individual sports? Answer: 18 Solution: Identify the two categorical variables: year level (Year 11, Year 12) and preferred activity (team sports, individual sports, no activity).
    Full step-by-step solution

    Step 1: Identify the two categorical variables: year level (Year 11, Year 12) and preferred activity (team sports, individual sports, no activity). Step 2: Create a two-way frequency table with year levels as rows and activity types as columns. | Team Sports | Individual Sports | No Activity | Row Total Year 11 | 13 | 7 | 5 | 25 Year 12 | 9 | 11 | 4 | 24 Column Total| 22 | 18 | 9 | 49 Step 3: To find the total number of students who prefer individual sports, add the frequencies in the 'Individual Sports' column: 7 (Year 11) + 11 (Year 12) = 18. The total number of students who prefer individual sports is 18.

  4. Kaia surveyed 56 students about their preferred method of learning: 24 prefer visual, 18 prefer auditory, and 14 prefer kinesthetic. Create a frequency table summarizing this categorical data. Answer: Visual: 24, Auditory: 18, Kinesthetic: 14 Solution: Identify the categories: Visual, Auditory, Kinesthetic. Visual | 24 Auditory | 18 Kinesthetic | 14 Total | 56 The answer is Visual: 24, Auditory: 18, Kinesthetic: 14.
    Full step-by-step solution

    Step 1: Identify the categories: Visual, Auditory, Kinesthetic. Step 2: Record the frequency for each category: - Visual: 24 students - Auditory: 18 students - Kinesthetic: 14 students Step 3: Verify the total: 24 + 18 + 14 = 56 students. Step 4: The completed frequency table is: Category | Frequency Visual | 24 Auditory | 18 Kinesthetic | 14 Total | 56 The answer is Visual: 24, Auditory: 18, Kinesthetic: 14.

  5. Isabella, a market researcher, surveyed 72 customers at a local farmers' market about their preferred fruit (Apples, Bananas, or Cherries) and whether they shop weekly (Yes or No). The results showed: 22 customers preferred Apples, 17 preferred Bananas, and the rest preferred Cherries. Of those who preferred Apples, 12 shop weekly. Of those who preferred Bananas, 7 shop weekly. Of those who preferred Cherries, 10 shop weekly. Construct a complete two-way frequency table summarizing the data, showing the counts for each combination of fruit preference and weekly shopping habit, along with row totals, column totals, and a grand total. Answer: See solution for completed table. Solution: Find the number who prefer Cherries. Total customers = 72 Apples = 22, Bananas = 17 Cherries = 72 - (22 + 17) = 72 - 39 = 33 Identify the given joint frequencies.
    Full step-by-step solution

    Step 1: Find the number who prefer Cherries. Total customers = 72 Apples = 22, Bananas = 17 Cherries = 72 - (22 + 17) = 72 - 39 = 33 Step 2: Identify the given joint frequencies. Apples & Weekly Yes = 12 Bananas & Weekly Yes = 7 Cherries & Weekly Yes = 10 Step 3: Calculate the missing joint frequencies (those who do not shop weekly). Apples & Weekly No = 22 - 12 = 10 Bananas & Weekly No = 17 - 7 = 10 Cherries & Weekly No = 33 - 10 = 23 Step 4: Calculate column totals. Weekly Yes total = 12 + 7 + 10 = 29 Weekly No total = 10 + 10 + 23 = 43 Step 5: Row totals (already known): Apples = 22, Bananas = 17, Cherries = 33 Step 6: Grand total = 29 + 43 = 72 (or sum of row totals: 22 + 17 + 33 = 72) Completed two-way frequency table: | Weekly Yes | Weekly No | Row Total ----------------------------------------------- Apples | 12 | 10 | 22 Bananas | 7 | 10 | 17 Cherries | 10 | 23 | 33 ----------------------------------------------- Column Total | 29 | 43 | 72 The answer is the completed table above.

  6. Emma surveyed 30 students about their favorite subject: 15 chose Math, 10 chose Science, and 5 chose English. Create a frequency table summarizing this data. Answer: Math: 15, Science: 10, English: 5 Solution: Identify the categories: Math, Science, English. Count the number of students for each category: Math = 15, Science = 10, English = 5.
    Full step-by-step solution

    Step 1: Identify the categories: Math, Science, English. Step 2: Count the number of students for each category: Math = 15, Science = 10, English = 5. Step 3: Create the frequency table: | Subject | Frequency | |---------|-----------| | Math | 15 | | Science | 10 | | English | 5 | The completed frequency table shows Math: 15, Science: 10, English: 5.