Question

This table displays the number of 10th and 11th-grade students who prefer either hip-hop or pop.


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)
• 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 like pop, you are more likely to be a 10th grader.
• If you are a 10th grader, you are more likely to prefer pop.

Answer 1

To analyze the data using relative frequencies, let's first summarize the information from the table:

- 10th Grade Hip-Hop: 112
- 10th Grade Pop: 53
- 10th Grade Total: 165
- 11th Grade Hip-Hop: 98
- 11th Grade Pop: 147
- 11th Grade Total: 245
- Overall Total: 410

Now, let’s calculate the relative frequencies for the relevant groups:

1. **If you like hip-hop, you are almost equally likely to be from 10th or 11th grade:**
- Total hip-hop fans: 112 (10th) + 98 (11th) = 210
- Proportion for 10th grade: 112 / 210 ≈ 0.533 (53.3%)
- Proportion for 11th grade: 98 / 210 ≈ 0.467 (46.7%)
This option is true—51% of hip-hop fans are in 10th grade, indicating a slight preference towards 10th graders.

2. **If you are an 11th grader, you are more likely to prefer hip-hop:**
- Proportion of 11th graders who prefer hip-hop: 98 / 245 ≈ 0.4 (40%)
- Proportion of 11th graders who prefer pop: 147 / 245 ≈ 0.6 (60%)
This option is false—11th graders are more likely to prefer pop.

3. **If you like pop, you are more likely to be a 10th grader:**
- Total pop fans: 53 (10th) + 147 (11th) = 200
- Proportion for 10th grade: 53 / 200 ≈ 0.265 (26.5%)
- Proportion for 11th grade: 147 / 200 ≈ 0.735 (73.5%)
This option is false—most pop fans are actually 11th graders.

4. **If you are a 10th grader, you are more likely to prefer pop:**
- Proportion of 10th graders who prefer pop: 53 / 165 ≈ 0.321 (32.1%)
- Proportion of 10th graders who prefer hip-hop: 112 / 165 ≈ 0.679 (67.9%)
This option is also false—most 10th graders prefer hip-hop.

Based on this analysis, the correct answer is:
**If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.**