Ask a New Question
Menu

Use the table to answer the question.

Music Preferences of 11th and 12th Grade Students
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 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 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 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.

1 answer

To analyze the statements regarding music preferences and grades using relative frequencies, we should calculate the proportions of students in each grade who prefer each music genre.

Given Data

  • 10th Grade Hip-Hop: 112
  • 10th Grade Pop: 53
  • 11th Grade Hip-Hop: 98
  • 11th Grade Pop: 147
  • Total Students: 410

Calculating Relative Frequencies

1. Music Preference for 10th and 11th Graders

  • Total for 10th Grade = 165
  • Total for 11th Grade = 245

Now calculate the relative frequencies for each preference.

For Hip-Hop:

  • 10th Graders: \( \frac{112}{165} \approx 0.6788 \) or 67.88%
  • 11th Graders: \( \frac{98}{245} \approx 0.40 \) or 40%

For Pop:

  • 10th Graders: \( \frac{53}{165} \approx 0.3212 \) or 32.12%
  • 11th Graders: \( \frac{147}{245} \approx 0.60 \) or 60%

Analyzing the Statements

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

    • False (40% for 11th graders prefer hip-hop vs 67.88% for 10th graders)

  2. If you like pop, you are more likely to be a 10th grader.

    • False (60% of 11th graders prefer pop vs 32.12% of 10th graders)

  3. If you are a 10th grader, you are more likely to prefer pop.

    • False (Only 32.12% of 10th graders prefer pop, while 60% of 11th graders prefer pop)

  4. If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.

    • To check:
      • Hip-Hop Total: 210
      • 10th Grade Hip-Hop: \( \frac{112}{210} \approx 0.5333 \) or 53.33%
      • 11th Grade Hip-Hop: \( \frac{98}{210} \approx 0.4667 \) or 46.67%

    This indicates that students who prefer hip-hop are indeed almost equally likely to be from either grade.

Conclusion

The correct statement is: If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.