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?.

Answer 1

To determine which student's results were closest to the class results, we first need to calculate the percentage of preferences in the total class results and compare it with each student's results.

The total preferences are 110 for vanilla and 190 for chocolate, making a total of \[ 110 + 190 = 300 \]

The overall percentages are:

• Percentage of seventh graders preferring vanilla: \[ \frac{110}{300} \times 100 \approx 36.67% \]

• Percentage of seventh graders preferring chocolate: \[ \frac{190}{300} \times 100 \approx 63.33% \]

Next, we need to calculate the percentages for each student's group:

1. Marcy's group:

   • Vanilla: 4, Chocolate: 6
   • Total: 10
   • Percentage of vanilla: \[ \frac{4}{10} \times 100 = 40% \]
   • Percentage of chocolate: \[ \frac{6}{10} \times 100 = 60% \]

2. Owen's group:

   • Vanilla: 3, Chocolate: 7
   • Total: 10
   • Percentage of vanilla: \[ \frac{3}{10} \times 100 = 30% \]
   • Percentage of chocolate: \[ \frac{7}{10} \times 100 = 70% \]

3. Spencer's group:

   • Vanilla: 1, Chocolate: 9
   • Total: 10
   • Percentage of vanilla: \[ \frac{1}{10} \times 100 = 10% \]
   • Percentage of chocolate: \[ \frac{9}{10} \times 100 = 90% \]

4. Vivian's group:

   • Vanilla: 2, Chocolate: 8
   • Total: 10
   • Percentage of vanilla: \[ \frac{2}{10} \times 100 = 20% \]
   • Percentage of chocolate: \[ \frac{8}{10} \times 100 = 80% \]

Now let's summarize the results:

• Class Results: 36.67% vanilla, 63.33% chocolate
• Marcy: 40% vanilla, 60% chocolate
• Owen: 30% vanilla, 70% chocolate
• Spencer: 10% vanilla, 90% chocolate
• Vivian: 20% vanilla, 80% chocolate

Now we calculate the differences from the class results:

1. Marcy:

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

2. Owen:

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

3. Spencer:

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

4. Vivian:

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

Comparing the total differences:

• Marcy: 6.66
• Owen: 13.34
• Spencer: 53.34
• Vivian: 33.34

The student whose results were closest to the class results is Marcy, with a total difference of 6.66%.