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Categorical Data

Grade 11 · Statistics · Worksheet 3

  1. Sophia surveyed students about their favorite music genres and created this two-way table showing preferences by gender: Music Genre Preferences Rock Hip-Hop Classical Total Male 12 8 5 25 Female 7 11 9 27 Total 19 19 14 52 What is the frequency of female students who prefer Classical music? Answer: ______________
  2. Ava surveyed 61 students at her school about their preferred method of communication and their grade level. The results are shown in the following bar chart description: For Grade 11 students, 16 prefer text, 11 prefer email, and 6 prefer phone. For Grade 12 students, 21 prefer text, 4 prefer email, and 3 prefer phone. Create a two-way frequency table summarizing the data by grade level and preferred communication method. Answer: ______________
  3. Ava surveyed 116 students at her school about their preferred method of exercise and their grade level. She found that 36 students preferred running, 41 preferred swimming, and 39 preferred cycling. Among the 56 juniors, 11 preferred running, 16 preferred swimming, and the rest preferred cycling. Among the seniors, 26 preferred cycling. Organize this data into a two-way frequency table with grade level (junior, senior) as rows and exercise preference (running, swimming, cycling) as columns. Then, determine how many seniors preferred running. Answer: ______________
  4. Emma surveyed 55 students about their favorite subject. 17 chose Math, 13 chose Science, 11 chose English, 9 chose History, and 5 chose Art. Create a frequency table summarizing this categorical data. Answer: ______________
  5. Emma surveyed students about their favorite subject: Math: 17, Science: 13, English: 9, History: 11. Create a frequency table summarizing the data. Answer: ______________
  6. Sophia surveyed 80 students at her school to investigate the relationship between their preferred type of beverage (coffee, tea, or juice) and their study habit (study in the morning or study in the evening). She found that 30 students prefer coffee, 28 prefer tea, and 22 prefer juice. Among those who prefer coffee, 18 study in the morning and the rest study in the evening. Among those who prefer tea, 16 study in the morning. Among those who prefer juice, 10 study in the evening. Construct a complete two-way frequency table summarizing this data, showing the counts of students for each combination of beverage preference and study habit, including row totals, column totals, and the grand total. Answer: ______________
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Answer Key & Explanations

Categorical Data · Grade 11 · Worksheet 3

  1. Sophia surveyed students about their favorite music genres and created this two-way table showing preferences by gender: Music Genre Preferences Rock Hip-Hop Classical Total Male 12 8 5 25 Female 7 11 9 27 Total 19 19 14 52 What is the frequency of female students who prefer Classical music? Answer: 9 Solution: Find the value at the intersection of the Female row and Classical column The table shows 9 female students prefer Classical music Therefore, the frequency is 9
    Full step-by-step solution

    Step 1: Identify the row for Female students in the table Step 2: Identify the column for Classical music Step 3: Find the value at the intersection of the Female row and Classical column Step 4: The table shows 9 female students prefer Classical music Step 5: Therefore, the frequency is 9

  2. Ava surveyed 61 students at her school about their preferred method of communication and their grade level. The results are shown in the following bar chart description: For Grade 11 students, 16 prefer text, 11 prefer email, and 6 prefer phone. For Grade 12 students, 21 prefer text, 4 prefer email, and 3 prefer phone. Create a two-way frequency table summarizing the data by grade level and preferred communication method. Answer: A two-way frequency table with rows for Grade 11 and Grade 12 and columns for Text, Email, and Phone, showing counts: Grade 11: Text=16, Email=11, Phone=6; Grade 12: Text=21, Email=4, Phone=3; Total Text=37, Total Email=15, Total Phone=9; Total Grade 11=33, Total Grade 12=28; Grand Total=61. Solution: Identify the two categorical variables: grade level (Grade 11, Grade 12) and preferred communication method (Text, Email, Phone). Set up a table with rows for grade levels and columns for communication methods.
    Full step-by-step solution

    Step 1: Identify the two categorical variables: grade level (Grade 11, Grade 12) and preferred communication method (Text, Email, Phone). Step 2: Set up a table with rows for grade levels and columns for communication methods. Add an extra row for column totals and an extra column for row totals. Step 3: Fill in the counts from the description: - Grade 11, Text: 16 - Grade 11, Email: 11 - Grade 11, Phone: 6 - Grade 12, Text: 21 - Grade 12, Email: 4 - Grade 12, Phone: 3 Step 4: Calculate row totals: Grade 11 total = 16 + 11 + 6 = 33; Grade 12 total = 21 + 4 + 3 = 28. Step 5: Calculate column totals: Text total = 16 + 21 = 37; Email total = 11 + 4 = 15; Phone total = 6 + 3 = 9. Step 6: Grand total = 33 + 28 = 61 (or 37 + 15 + 9 = 61). Step 7: Present the completed two-way frequency table: | Text | Email | Phone | Total ----------------------------------------- Grade 11 | 16 | 11 | 6 | 33 Grade 12 | 21 | 4 | 3 | 28 ----------------------------------------- Total | 37 | 15 | 9 | 61 The answer is the completed table above.

  3. Ava surveyed 116 students at her school about their preferred method of exercise and their grade level. She found that 36 students preferred running, 41 preferred swimming, and 39 preferred cycling. Among the 56 juniors, 11 preferred running, 16 preferred swimming, and the rest preferred cycling. Among the seniors, 26 preferred cycling. Organize this data into a two-way frequency table with grade level (junior, senior) as rows and exercise preference (running, swimming, cycling) as columns. Then, determine how many seniors preferred running. Answer: 25 Solution: Set up a two-way frequency table with rows for Junior and Senior, and columns for Running, Swimming, and Cycling. Include row totals and column totals. - Total juniors = 56 - Juniors who prefer running = 11 - Juniors who prefer swimming = 16 - Juniors who prefer cycling = 56 - 11 - 16 = 29 Total…
    Full step-by-step solution

    Step 1: Set up a two-way frequency table with rows for Junior and Senior, and columns for Running, Swimming, and Cycling. Include row totals and column totals. Step 2: Fill in known values: - Total juniors = 56 - Juniors who prefer running = 11 - Juniors who prefer swimming = 16 - Juniors who prefer cycling = 56 - 11 - 16 = 29 Step 3: Total running = 36, so seniors who prefer running = 36 - 11 = 25 - Total swimming = 41, so seniors who prefer swimming = 41 - 16 = 25 - Total cycling = 39, seniors who prefer cycling = 26 (given) Step 4: Total seniors = 25 + 25 + 26 = 76 - Check total students = 56 + 76 = 116, which matches the total. Step 5: The two-way frequency table is: Running Swimming Cycling Total Junior 11 16 29 56 Senior 25 25 26 76 Total 36 41 39 116 The number of seniors who preferred running is 25. The answer is 25.

  4. Emma surveyed 55 students about their favorite subject. 17 chose Math, 13 chose Science, 11 chose English, 9 chose History, and 5 chose Art. Create a frequency table summarizing this categorical data. Answer: Math: 17, Science: 13, English: 11, History: 9, Art: 5 Solution: The frequency table is: Math: 17, Science: 13, English: 11, History: 9, Art: 5
    Full step-by-step solution

    Step 1: Identify the categories: Math, Science, English, History, Art Step 2: List the frequency for each category: - Math: 17 - Science: 13 - English: 11 - History: 9 - Art: 5 Step 3: Verify the total: 17 + 13 + 11 + 9 + 5 = 55, which matches the total number of students surveyed. The frequency table is: Math: 17, Science: 13, English: 11, History: 9, Art: 5

  5. Emma surveyed students about their favorite subject: Math: 17, Science: 13, English: 9, History: 11. Create a frequency table summarizing the data. Answer: Math: 17, Science: 13, English: 9, History: 11 Solution: Identify the categories: Math, Science, English, History. List the corresponding frequencies: 17, 13, 9, 11.
    Full step-by-step solution

    Step 1: Identify the categories: Math, Science, English, History. Step 2: List the corresponding frequencies: 17, 13, 9, 11. Step 3: Construct the frequency table: | Subject | Frequency | |----------|-----------| | Math | 17 | | Science | 13 | | English | 9 | | History | 11 | The summarized data is Math: 17, Science: 13, English: 9, History: 11.

  6. Sophia surveyed 80 students at her school to investigate the relationship between their preferred type of beverage (coffee, tea, or juice) and their study habit (study in the morning or study in the evening). She found that 30 students prefer coffee, 28 prefer tea, and 22 prefer juice. Among those who prefer coffee, 18 study in the morning and the rest study in the evening. Among those who prefer tea, 16 study in the morning. Among those who prefer juice, 10 study in the evening. Construct a complete two-way frequency table summarizing this data, showing the counts of students for each combination of beverage preference and study habit, including row totals, column totals, and the grand total. Answer: A two-way frequency table with rows for Coffee, Tea, Juice and columns for Morning, Evening, and Total: Coffee (18, 12, 30), Tea (16, 12, 28), Juice (12, 10, 22), and totals (46, 34, 80). Solution: Set up the table structure with rows for beverage preference (Coffee, Tea, Juice) and columns for study habit (Morning, Evening), plus a row for column totals and a column for row totals. Coffee 18 12 30 Tea 16 12 28 Juice 12 10…
    Full step-by-step solution

    Step 1: Set up the table structure with rows for beverage preference (Coffee, Tea, Juice) and columns for study habit (Morning, Evening), plus a row for column totals and a column for row totals. Step 2: Fill in the given values: - Coffee & Morning: 18 - Coffee row total: 30 - Tea & Morning: 16 - Tea row total: 28 - Juice row total: 22 - Juice & Evening: 10 Step 3: Calculate missing cell values: - Coffee & Evening: 30 - 18 = 12 - Tea & Evening: 28 - 16 = 12 - Juice & Morning: 22 - 10 = 12 Step 4: Calculate column totals: - Morning total: 18 + 16 + 12 = 46 - Evening total: 12 + 12 + 10 = 34 Step 5: Verify grand total: 46 + 34 = 80, and 30 + 28 + 22 = 80. The completed two-way frequency table is: Morning Evening Total Coffee 18 12 30 Tea 16 12 28 Juice 12 10 22 Total 46 34 80 The final answer is the table shown above.