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. 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?

Answer 1

To determine which student's results were closest to the class results, we will first find the percentages of vanilla and chocolate preferences for each group and then compare them to the overall totals of 110 vanilla and 190 chocolate.

1. Total Responses: The class results show:

   • Total vanilla: 110
   • Total chocolate: 190
   • Total respondents = 110 + 190 = 300

2. Overall Preferences Percentages: \[ \text{Percentage of vanilla} = \frac{110}{300} = \frac{11}{30} \approx 0.3667 \text{ (or 36.67%)} \] \[ \text{Percentage of chocolate} = \frac{190}{300} = \frac{19}{30} \approx 0.6333 \text{ (or 63.33%)} \]

3. Group Preferences: Next, we calculate the percentages for each student’s group:

   • Marcy’s group:

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

   • Owen’s group:

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

   • Spencer’s group:

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

   • Vivian’s group:

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

4. Comparing Results: Now we compare each student's group's percentage of vanilla to the class's overall percentage of vanilla (approx. 36.67%):

   • Marcy’s group: 40% (difference of 3.33%)
   • Owen’s group: 30% (difference of 6.67%)
   • Spencer’s group: 10% (difference of 26.67%)
   • Vivian’s group: 20% (difference of 16.67%)

5. Conclusion: Marcy's group, with 40% preference for vanilla, has the smallest difference from the overall class percentage of 36.67%. Therefore, Marcy’s results were closest to the class results.