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: 35 which of the following is a correct two - way frequency table for the data? four two - way frequency tables are presented with columns for grades 9 - 10, grades 11 - 12, and total, and rows for rap, rock, country, and total, with different numerical values in each table

Explanation:

Step1: Check Rap totals

For Rap, Grades 9 - 10: 40, Grades 11 - 12: 60. Total Rap should be \(40 + 60 = 100\).

Step2: Check Rock totals

For Rock, Grades 9 - 10: 30, Grades 11 - 12: 25. Total Rock should be \(30 + 25 = 55\).

Step3: Check Country totals

For Country, Grades 9 - 10: 55, Grades 11 - 12: 35. Total Country should be \(55 + 35 = 90\).

Step4: Check grade totals

Grades 9 - 10 total: \(40 + 30 + 55 = 125\). Grades 11 - 12 total: \(60 + 25 + 35 = 120\). Grand total: \(125 + 120 = 245\). Now check each table:

• First table (leftmost): Rap total \(55 + 35 = 90\) (wrong, should be 100). Eliminate.
• Second table: Rap total \(35 + 55 = 90\) (wrong). Eliminate.
• Third table: Rap total \(60 + 40 = 100\) (good), Rock total \(25 + 30 = 55\) (good), Country total \(35 + 55 = 90\) (good), Grades 9 - 10: \(60 + 25 + 35 = 120\) (wrong, should be 125). Eliminate.
• Fourth table (rightmost? Wait, let's re - check. Wait, first table (from right, first): Rap: 40 (9 - 10) + 60 (11 - 12) = 100, Rock: 30 + 25 = 55, Country: 55 + 35 = 90, Grades 9 - 10: 40 + 30 + 55 = 125, Grades 11 - 12: 60 + 25 + 35 = 120. This matches. Wait, maybe I mis - numbered. Let's list the four tables:

Table 1 (rightmost):
Rap: 40 (9 - 10), 60 (11 - 12), total 100
Rock: 30 (9 - 10), 25 (11 - 12), total 55
Country: 55 (9 - 10), 35 (11 - 12), total 90
Grades 9 - 10: 40 + 30 + 55 = 125
Grades 11 - 12: 60 + 25 + 35 = 120
Grand total: 125 + 120 = 245. This matches all totals.

Answer:

The right - most table (the first table from the right)