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High school students from grades 9–10 and 11–12 were asked to choose the kind of band to have play at a school dance: rap, rock, or country.

Their choices were as follows:
Grades 9–10—Rap: 40; Rock: 30; Country: 55
Grades 11–12—Rap: 60; Rock: 25; Country: 35

Which of the following is a correct two-way frequency table for the data?

Band Preference for School Dance
Rap Rock Country Row totals
Grades 9–10 0.28 0.21 0.38 0.86
Grades 11–12 0.41 0.17 0.24 0.83
Column totals 0.69 0.38 0.62 1

Band Preference for School Dance
Rap Rock Country Row totals
Grades 9–10 0.40 0.55 0.61 0.86
Grades 11–12 0.60 0.45 0.39 0.83
Column totals 1 1 1 1

Band Preference for School Dance
Rap Rock Country Row totals
Grades 9–10 40 30 55 125
Grades 11–12 60 25 35 120
Column totals 100 55 90 245

Band Preference for School Dance
Rap Rock Country Row totals
Grades 9–10 0.32 0.24 0.44 1
Grades 11–12 0.50 0.21 0.29 1
Column totals 0.69 0.38 0.62 1

1 answer

To create a correct two-way frequency table based on the band preferences of students in grades 9-10 and 11-12, we first need to summarize the data provided.

From the data given:

  • Grades 9-10:

    • Rap: 40
    • Rock: 30
    • Country: 55
    • Row Total (Grades 9-10): 40 + 30 + 55 = 125

  • Grades 11-12:

    • Rap: 60
    • Rock: 25
    • Country: 35
    • Row Total (Grades 11-12): 60 + 25 + 35 = 120

Now we'll compute the column totals:

  • Total for Rap: 40 (Grades 9-10) + 60 (Grades 11-12) = 100
  • Total for Rock: 30 (Grades 9-10) + 25 (Grades 11-12) = 55
  • Total for Country: 55 (Grades 9-10) + 35 (Grades 11-12) = 90

Now we can list out the entire frequency table:

| Band Preference for School Dance | Rap | Rock | Country | Row Totals | |----------------------------------|-----|------|---------|------------| | Grades 9-10 | 40 | 30 | 55 | 125 | | Grades 11-12 | 60 | 25 | 35 | 120 | | Column Totals | 100 | 55 | 90 | 245 |

Among the options you presented, it appears that option 3, which reports the counts rather than percentages, is the only one that correctly represents the data provided:

"Band Preference for School Dance Rap: 40, Rock: 30, Country: 55, Row Total: 125 Rap: 60, Rock: 25, Country: 35, Row Total: 120 Column Totals: 100, 55, 90, 245"

This matches the actual counts exactly, and thus is the correct two-way frequency table for the data.