Question

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: 40 which of the following is a correct two - way relative frequency table for the data? tables are shown with different frequency distributions for rap, rock, country across grades 9 - 10, grades 11 - 12, and total

Explanation:

Step1: Calculate total students

Total students = Grades 9 - 10 total + Grades 11 - 12 total = (40 + 30 + 55) + (60 + 25 + 40) = 125 + 125 = 250.

Step2: Check relative frequencies for each table

For a two - way relative frequency table, each cell should be the frequency divided by total (250), multiplied by 100 to get percentage.

• For Rap in Grades 9 - 10: $\frac{40}{250}\times100 = 16\%$? Wait, no, wait the first table (let's check the second from left? Wait, the correct approach is:

First, let's list the frequencies:
Grades 9 - 10: Rap = 40, Rock = 30, Country = 55; Total = 40 + 30 + 55 = 125
Grades 11 - 12: Rap = 60, Rock = 25, Country = 40; Total = 60+25 + 40=125
Total overall: 250

Now, calculate relative frequencies (percentage of total):

• Rap, Grades 9 - 10: $\frac{40}{250}\times100 = 16\%$? Wait no, wait the table with percentages: Let's check the second table from the left (the one with Rap: 16%, Rock:12%, Country:22% for Grades 9 - 10; Rap:24%, Rock:10%, Country:16% for Grades 11 - 12; Totals: 40%, 22%, 38%). Wait, no, let's recalculate:

For Grades 9 - 10:
Rap: $\frac{40}{250}\times100 = 16\%$
Rock: $\frac{30}{250}\times100 = 12\%$
Country: $\frac{55}{250}\times100 = 22\%$
Total for Grades 9 - 10: $\frac{125}{250}\times100 = 50\%$

For Grades 11 - 12:
Rap: $\frac{60}{250}\times100 = 24\%$
Rock: $\frac{25}{250}\times100 = 10\%$
Country: $\frac{40}{250}\times100 = 16\%$
Total for Grades 11 - 12: $\frac{125}{250}\times100 = 50\%$

For overall totals:
Rap: $\frac{40 + 60}{250}\times100=\frac{100}{250}\times100 = 40\%$
Rock: $\frac{30+25}{250}\times100=\frac{55}{250}\times100 = 22\%$
Country: $\frac{55 + 40}{250}\times100=\frac{95}{250}\times100 = 38\%$ (Wait, but in the table, the second from left has Country total 38%). Wait, the table with:
Rap: Grades 9 - 10:16%, Grades 11 - 12:24%, Total:40%
Rock: Grades 9 - 10:12%, Grades 11 - 12:10%, Total:22%
Country: Grades 9 - 10:22%, Grades 11 - 12:16%, Total:38%
Total rows: 50%, 50%, 100%

Let's verify each cell:

• Rap, Grades 9 - 10: $\frac{40}{250}\times100 = 16\%$ ✔️
• Rap, Grades 11 - 12: $\frac{60}{250}\times100 = 24\%$ ✔️
• Rap, Total: $\frac{100}{250}\times100 = 40\%$ ✔️
• Rock, Grades 9 - 10: $\frac{30}{250}\times100 = 12\%$ ✔️
• Rock, Grades 11 - 12: $\frac{25}{250}\times100 = 10\%$ ✔️
• Rock, Total: $\frac{55}{250}\times100 = 22\%$ ✔️
• Country, Grades 9 - 10: $\frac{55}{250}\times100 = 22\%$ ✔️
• Country, Grades 11 - 12: $\frac{40}{250}\times100 = 16\%$ ✔️
• Country, Total: $\frac{95}{250}\times100 = 38\%$ ✔️
• Grades 9 - 10 Total: $\frac{125}{250}\times100 = 50\%$ ✔️
• Grades 11 - 12 Total: $\frac{125}{250}\times100 = 50\%$ ✔️
• Overall Total: 100% ✔️

So the correct two - way relative frequency table is the second one from the left (the one with Rap:16%, Rock:12%, Country:22% for Grades 9 - 10; Rap:24%, Rock:10%, Country:16% for Grades 11 - 12; Totals:40%, 22%, 38% and row totals 50%, 50%, 100%).

Answer:

The second table from the left (the table with Grades 9 - 10 Rap:16%, Rock:12%, Country:22%; Grades 11 - 12 Rap:24%, Rock:10%, Country:16%; Totals:40%, 22%, 38% and row totals 50%, 50%, 100%)