Use the table to answer the question.
Hip-Hop Pop Totals
10th Grade 112 53 165
11th Grade 98 147 245
Total 210 200 410
Examine the data from a survey of 10th and 11th graders about which music genre they prefer.
Using relative frequencies, which of the following is true?
(1 point)
Responses
If you like pop, you are more likely to be a 10th grader.
If you like pop, you are more likely to be a 10th grader.
If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.
If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.
If you are an 11th grader, you are more likely to prefer hip-hop.
If you are an 11th grader, you are more likely to prefer hip-hop.
If you are a 10th grader, you are more likely to prefer pop.
If you are a 10th grader, you are more likely to prefer pop.
To determine the answer using relative frequencies, we need to calculate the proportions of each music genre for each grade.
The relative frequency can be calculated by dividing the number of individuals in each category by the total number of individuals in that grade.
For 10th Grade:
- Relative frequency of Hip-Hop = 112/165 ≈ 0.679
- Relative frequency of Pop = 53/165 ≈ 0.321
For 11th Grade:
- Relative frequency of Hip-Hop = 98/245 ≈ 0.4
- Relative frequency of Pop = 147/245 ≈ 0.6
Comparing the relative frequencies, we can determine the following:
- If you like pop, you are more likely to be an 11th grader because the relative frequency of Pop is higher in the 11th grade (0.6) compared to the 10th grade (0.321).
- If you like hip-hop, you are almost equally likely to be from 10th or 11th grade because the relative frequencies of Hip-Hop are similar for both grades (0.679 for 10th grade, 0.4 for 11th grade).
Therefore, the correct answer is:
If you like pop, you are more likely to be an 11th grader.
To determine which statement is true using relative frequencies, we need to compare the proportions of each music genre within each grade level.
To calculate the relative frequency for each music genre within a specific grade level, we divide the count of that genre by the total count of that grade level.
For example, the relative frequency of pop among 10th graders is calculated as:
Relative frequency of pop among 10th graders = Count of pop among 10th graders / Total count of 10th graders
= 53 / 165
= 0.3212 (rounded to four decimal places)
By performing similar calculations, we can find the relative frequencies for the other music genres in each grade level.
The relative frequencies for each music genre among 10th and 11th graders are as follows:
10th Grade:
- Hip-Hop: 112 / 165 ≈ 0.6788
- Pop: 53 / 165 ≈ 0.3212
11th Grade:
- Hip-Hop: 98 / 245 ≈ 0.4
- Pop: 147 / 245 ≈ 0.6
Now, let's analyze the relative frequencies to determine which statement is true:
1. If you like pop, you are more likely to be a 10th grader.
This statement is false. The relative frequency of pop among 10th graders is approximately 0.3212, while the relative frequency of pop among 11th graders is approximately 0.6, which is higher.
2. If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.
This statement is true. The relative frequency of hip-hop among 10th graders is approximately 0.6788, and among 11th graders, it is approximately 0.4. Although not exactly equal, the difference is relatively small.
3. If you are an 11th grader, you are more likely to prefer hip-hop.
This statement is true. The relative frequency of hip-hop among 11th graders is approximately 0.4, while the relative frequency among 10th graders is approximately 0.6788, which is higher.
4. If you are a 10th grader, you are more likely to prefer pop.
This statement is false. The relative frequency of pop among 10th graders is approximately 0.3212, while the relative frequency of pop among 11th graders is approximately 0.6, which is higher.
Based on the calculations of relative frequencies, the correct statement is:
"If you like hip-hop, you are almost equally likely to be from 10th or 11th grade."