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Use the table to answer the 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 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 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.

1 answer

To analyze the data using relative frequencies, we first need to calculate the proportions of 10th and 11th graders within each music genre.

Given Data:

Total Students:

  • 10th Grade: 165
  • 11th Grade: 245
  • Total: 410

Preferences:

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

Relative Frequencies Calculation:

  1. For 10th Graders:

    • Hip-Hop: \( \frac{112}{165} \approx 0.6788 \) (about 67.88%)
    • Pop: \( \frac{53}{165} \approx 0.3212 \) (about 32.12%)

  2. For 11th Graders:

    • Hip-Hop: \( \frac{98}{245} \approx 0.4 \) (about 40%)
    • Pop: \( \frac{147}{245} \approx 0.6 \) (about 60%)

  3. For Total Hip-Hop:

    • Total Preference for Hip-Hop: \( \frac{210}{410} \approx 0.5122 \) (about 51.22%)
    • 10th Grader Hip-Hop Distribution: \( \frac{112}{210} \approx 0.5333 \) (about 53.33%)
    • 11th Grader Hip-Hop Distribution: \( \frac{98}{210} \approx 0.4667 \) (about 46.67%)

  4. For Total Pop:

    • Total Preference for Pop: \( \frac{200}{410} \approx 0.4878 \) (about 48.78%)
    • 10th Grader Pop Distribution: \( \frac{53}{200} \approx 0.265 \) (about 26.5%)
    • 11th Grader Pop Distribution: \( \frac{147}{200} \approx 0.735 \) (about 73.5%)

Conclusions from the Calculated Relative Frequencies:

  • If you are a 10th grader, you are more likely to prefer pop. (False, as about 67.88% prefer hip-hop)
  • If you are an 11th grader, you are more likely to prefer hip-hop. (False, as about 60% prefer pop)
  • If you like hip-hop, you are almost equally likely to be from 10th or 11th grade. (False; about 53.33% are 10th graders and 46.67% are 11th graders.)
  • If you like pop, you are more likely to be a 10th grader. (False; 73.5% of pop fans are 11th graders.)

Therefore, none of the statements presented are true based on the relative frequency calculations.