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Each student in Mrs. Halstead's class was assigned a random group of 10 seventh graders, They asked everyone in each group the following question: "Do you prefer vanilla or chocolate ice cream?" The results of some of the students' finding sare shown below.

Marcys group: 4 vanilla and 6 chocolate
Owen's group: 3 vannilla and 7 chocolate
Spencers group: 1 vanilla and 9 chocolate
Vivian's group: 2 vanilla and 8 chocolate

When the class combined all of the results, they found that 110 seventh graders preferred vanilla and 190 preferred chcoclate. Which student's results were closet to the class results?

1 answer

To determine which student's results were closest to the class results, we can first calculate the percentage of vanilla and chocolate preferences in each student's group and then compare them to the overall class preferences.

  1. Marcys group:

    • Vanilla: 4
    • Chocolate: 6
    • Total: 10
    • Vanilla percentage = \( \frac{4}{10} \times 100 = 40% \)
    • Chocolate percentage = \( \frac{6}{10} \times 100 = 60% \)

  2. Owen's group:

    • Vanilla: 3
    • Chocolate: 7
    • Total: 10
    • Vanilla percentage = \( \frac{3}{10} \times 100 = 30% \)
    • Chocolate percentage = \( \frac{7}{10} \times 100 = 70% \)

  3. Spencer's group:

    • Vanilla: 1
    • Chocolate: 9
    • Total: 10
    • Vanilla percentage = \( \frac{1}{10} \times 100 = 10% \)
    • Chocolate percentage = \( \frac{9}{10} \times 100 = 90% \)

  4. Vivian's group:

    • Vanilla: 2
    • Chocolate: 8
    • Total: 10
    • Vanilla percentage = \( \frac{2}{10} \times 100 = 20% \)
    • Chocolate percentage = \( \frac{8}{10} \times 100 = 80% \)

Overall class results:

  • Total students surveyed = 110 (Vanilla) + 190 (Chocolate) = 300
  • Vanilla percentage = \( \frac{110}{300} \times 100 \approx 36.67% \)
  • Chocolate percentage = \( \frac{190}{300} \times 100 \approx 63.33% \)

Now let's compare each group's percentages to the overall class percentages:

  • Marcys group (40% Vanilla, 60% Chocolate):

    • Difference: |40% - 36.67%| = 3.33% for Vanilla
    • Difference: |60% - 63.33%| = 3.33% for Chocolate
    • Total difference = \( 3.33% + 3.33% = 6.66% \)

  • Owen's group (30% Vanilla, 70% Chocolate):

    • Difference: |30% - 36.67%| = 6.67% for Vanilla
    • Difference: |70% - 63.33%| = 6.67% for Chocolate
    • Total difference = \( 6.67% + 6.67% = 13.34% \)

  • Spencer's group (10% Vanilla, 90% Chocolate):

    • Difference: |10% - 36.67%| = 26.67% for Vanilla
    • Difference: |90% - 63.33%| = 26.67% for Chocolate
    • Total difference = \( 26.67% + 26.67% = 53.34% \)

  • Vivian's group (20% Vanilla, 80% Chocolate):

    • Difference: |20% - 36.67%| = 16.67% for Vanilla
    • Difference: |80% - 63.33%| = 16.67% for Chocolate
    • Total difference = \( 16.67% + 16.67% = 33.34% \)

Conclusion: Marcys group had the smallest total difference of 6.66%, which means that Marcys results were closest to the class results.