A sample of 245 high school students from grades [tex]$9-10$[/tex] and [tex]$11-12$[/tex] were asked to choose the kind of band to have play at a school dance: rap, rock, or country. [tex]$51 \%$[/tex] of the sample is grades [tex]$9-10$[/tex]. From the sample, it is determined that [tex]$16.3 \%$[/tex] were students in grades [tex]$9-10$[/tex] who prefer a rap band and [tex]$22.4 \%$[/tex] were students in grades [tex]$9-10$[/tex] who prefer a country band. [tex]$14.3 \%$[/tex] were of students in grades [tex]$11-12$[/tex] who prefer a country band, while [tex]$10.2 \%$[/tex] were students in grades [tex]$11-12$[/tex] who prefer a rock band. The most popular choice was rap, with [tex]$40.8 \%$[/tex] of students making it their preferred option.
Which of the following is a correct two-way relative frequency table for the data?
School Dance Band Preference
& Rap & Rock & Country & Row totals
Grades 9-10 & 16.3 & 12.2 & 22.4 & 51
Grades 11-12 & 24.5 & 10.2 & 14.3 & 49
Column totals & 40.8 & 22.4 & 36.7 & 100
School Dance Band Preference
& Rap & Rock & Country & Row totals
Grades 9-10 & [tex]$16.3 \%$[/tex] & [tex]$12.3 \%$[/tex] & [tex]$22.4 \%$[/tex] & [tex]$51 \%$[/tex]
Grades 11-12 & [tex]$24.5 \%$[/tex] & [tex]$10.2 \%$[/tex] & [tex]$14.3 \%$[/tex] & [tex]$49 \%$[/tex]
Column totals & [tex]$40.8 \%$[/tex] & [tex]$22.5 \%$[/tex] & [tex]$36.7 \%$[/tex] & [tex]$100 \%$[/tex]
School Dance Band Preference
& Rap & Rock & Country & Row totals
Answer (2)
Calculate the percentage of students in grades 11-12: 100% − 51% = 49% .
Calculate the percentage of students in grades 9-10 who prefer rock: 51% − 16.3% − 22.4% = 12.3% .
Calculate the percentage of students in grades 11-12 who prefer rap: 49% − 10.2% − 14.3% = 24.5% .
The correct table is the one with the following values: Grades 9-10 (Rap: 16.3% , Rock: 12.3% , Country: 22.4% ), Grades 11-12 (Rap: 24.5% , Rock: 10.2% , Country: 14.3% ), Column totals (Rap: 40.8% , Rock: 22.5% , Country: 36.7% ).
Explanation
Analyze the given data Let's analyze the given information to determine the correct two-way relative frequency table. We are given the following:
51% of the students are in grades 9-10.
16.3% of the students are in grades 9-10 and prefer rap.
22.4% of the students are in grades 9-10 and prefer country.
14.3% of the students are in grades 11-12 and prefer country.
10.2% of the students are in grades 11-12 and prefer rock.
40.8% of the students prefer rap.
Calculate percentage of students in grades 11-12 First, we can calculate the percentage of students in grades 11-12: 100% − 51% = 49% So, 49% of the students are in grades 11-12.
Calculate percentage of students in grades 9-10 who prefer rock Next, we can calculate the percentage of students in grades 9-10 who prefer rock: 51% − 16.3% − 22.4% = 12.3% So, 12.3% of the students are in grades 9-10 and prefer rock.
Calculate percentage of students in grades 11-12 who prefer rap Now, we can calculate the percentage of students in grades 11-12 who prefer rap: 49% − 10.2% − 14.3% = 24.5% So, 24.5% of the students are in grades 11-12 and prefer rap.
Calculate total percentage of students who prefer country We can also calculate the total percentage of students who prefer country: 22.4% + 14.3% = 36.7% So, 36.7% of the students prefer country.
Calculate total percentage of students who prefer rock Finally, we can calculate the total percentage of students who prefer rock: 100% − 40.8% − 36.7% = 22.5% So, 22.5% of the students prefer rock.
Compare calculated values with the tables Now, let's compare these calculated values with the values in the provided tables. The first table is:
Rap
Rock
Country
Row totals
Grades 9-10
16.3
12.2
22.4
51
Grades 11-12
24.5
10.2
14.3
49
Column totals
40.8
22.4
36.7
100
The second table is:
Rap
Rock
Country
Row totals
Grades 9-10
16.3%
12.3%
22.4%
51%
Grades 11-12
24.5%
10.2%
14.3%
49%
Column totals
40.8%
22.5%
36.7%
100%
Comparing the calculated values with the tables, we see that the second table accurately represents the data.
State the final answer The correct two-way relative frequency table is:
Rap
Rock
Country
Row totals
Grades 9-10
16.3%
12.3%
22.4%
51%
Grades 11-12
24.5%
10.2%
14.3%
49%
Column totals
40.8%
22.5%
36.7%
100%
Examples
Two-way relative frequency tables are useful in market research to analyze customer preferences across different demographics. For example, a company might survey customers to understand their preferred product features based on age group. The table helps visualize the relationships between these variables, enabling targeted marketing strategies.
The correct two-way relative frequency table for the band preferences among students in grades 9-10 and 11-12 matches the second option presented. The percentages are calculated accurately, reflecting the preferences among the groups. The final values show that 16.3% of 9-10 prefer rap, along with corresponding values for all categories.
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