Use the table to answer the question.

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)
Responses

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.

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 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 are an 11th grader, you are more likely to prefer hip-hop.

Answer 1

To analyze the data using relative frequencies, we need to calculate the proportion of preferences for each music genre within each grade.

1. For 10th graders:

   • Total 10th graders = 165
   • Preferring Hip-Hop = 112
   • Preferring Pop = 53

   Relative frequency for 10th graders preferring Hip-Hop: \[ \text{Relative frequency (10th Hip-Hop)} = \frac{112}{165} \approx 0.6788 \text{ (or 67.88%)} \] Relative frequency for 10th graders preferring Pop: \[ \text{Relative frequency (10th Pop)} = \frac{53}{165} \approx 0.3212 \text{ (or 32.12%)} \]

   Conclusion for 10th graders: More likely to prefer Hip-Hop.

2. For 11th graders:

   • Total 11th graders = 245
   • Preferring Hip-Hop = 98
   • Preferring Pop = 147

   Relative frequency for 11th graders preferring Hip-Hop: \[ \text{Relative frequency (11th Hip-Hop)} = \frac{98}{245} \approx 0.4 \text{ (or 40%)} \] Relative frequency for 11th graders preferring Pop: \[ \text{Relative frequency (11th Pop)} = \frac{147}{245} \approx 0.6 \text{ (or 60%)} \]

   Conclusion for 11th graders: More likely to prefer Pop.

3. To compare hip-hop preference across grades (total hip-hop preference):

   • Total preferring Hip-Hop = 210
   • 10th graders preferring Hip-Hop = 112
   • 11th graders preferring Hip-Hop = 98

   Relative frequency of hip-hop preference: \[ \text{Relative frequency (Hip-Hop from 10th)} = \frac{112}{210} \approx 0.5333 \text{ (or 53.33%)} \] \[ \text{Relative frequency (Hip-Hop from 11th)} = \frac{98}{210} \approx 0.4667 \text{ (or 46.67%)} \]

   Conclusion for hip-hop: If you like hip-hop, you are more likely (53.33%) to be from 10th grade.

4. To compare pop preference across grades (total pop preference):

   • Total preferring Pop = 200
   • 10th graders preferring Pop = 53
   • 11th graders preferring Pop = 147

   Relative frequency of pop preference: \[ \text{Relative frequency (Pop from 10th)} = \frac{53}{200} \approx 0.265 \text{ (or 26.5%)} \] \[ \text{Relative frequency (Pop from 11th)} = \frac{147}{200} \approx 0.735 \text{ (or 73.5%)} \]

   Conclusion for pop: If you like pop, you are more likely to be from 11th grade.

Summary of Findings:

• 10th graders prefer Hip-Hop.
• 11th graders prefer Pop.
• If you like Hip-Hop, you are more likely to be from 10th grade.
• If you like Pop, you are more likely to be from 11th grade.

Final Answer:

If you are an 11th grader, you are more likely to prefer hip-hop. (This statement is false based on frequency results, while the observation about 10th graders being associated with Hip-Hop is true.)

Among the provided options, the correct conclusion from relative frequencies is: If you like hip-hop, you are almost equally likely to be from 10th or 11th grade. (This, however, should consider revised total preferences; 10th is comparatively high.)