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' findings are shown below.

Question

Marcy’s group: 4 vanilla and 6 chocolate
Owen’s group: 3 vanilla and 7 chocolate
Spencer’s 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 chocolate. Which student’s results were closest to the class results?

A.
Marcy

B.
Owen

C.
Spencer

D.
Vivian

Answer 1

To determine which student's results were closest to the class results, we can first analyze the proportion of vanilla and chocolate preferences in each student's group compared to the overall class results.

Class Results

• Total vanilla preferences: 110
• Total chocolate preferences: 190

Total responses = 110 + 190 = 300 students.

Proportions for the class:

• Proportion of vanilla = \( \frac{110}{300} = \frac{11}{30} \) (approximately 36.67%)
• Proportion of chocolate = \( \frac{190}{300} = \frac{19}{30} \) (approximately 63.33%)

Individual Groups

Next, we calculate the proportions for each individual student’s group:

1. Marcy’s group:

   • Vanilla: 4, Chocolate: 6
   • Total: 10
   • Proportion of vanilla = \( \frac{4}{10} = 0.4 \) or 40%
   • Proportion of chocolate = \( \frac{6}{10} = 0.6 \) or 60%

2. Owen’s group:

   • Vanilla: 3, Chocolate: 7
   • Total: 10
   • Proportion of vanilla = \( \frac{3}{10} = 0.3 \) or 30%
   • Proportion of chocolate = \( \frac{7}{10} = 0.7 \) or 70%

3. Spencer’s group:

   • Vanilla: 1, Chocolate: 9
   • Total: 10
   • Proportion of vanilla = \( \frac{1}{10} = 0.1 \) or 10%
   • Proportion of chocolate = \( \frac{9}{10} = 0.9 \) or 90%

4. Vivian’s group:

   • Vanilla: 2, Chocolate: 8
   • Total: 10
   • Proportion of vanilla = \( \frac{2}{10} = 0.2 \) or 20%
   • Proportion of chocolate = \( \frac{8}{10} = 0.8 \) or 80%

Comparing Proportions

We now compare the proportions for vanilla from each group to the class proportions:

• Marcy's group: 40% vanilla (close to 36.67%)
• Owen's group: 30% vanilla (further from 36.67%)
• Spencer's group: 10% vanilla (far from 36.67%)
• Vivian's group: 20% vanilla (far from 36.67%)

By comparing how close each group's vanilla proportion is to the class average:

• Marcy: \( |40 - 36.67| = 3.33 \)
• Owen: \( |30 - 36.67| = 6.67 \)
• Spencer: \( |10 - 36.67| = 26.67 \)
• Vivian: \( |20 - 36.67| = 16.67 \)

Conclusion

The student whose results were closest to the class results is Marcy with a difference of 3.33%.

Thus, the answer is A. Marcy.