Questions: The ages and grades of some of the 17 girls on a club soccer team are shown in the table. 15 years old 16 years old ------------------------------------- 9th grade 2 0 10th grade 10 Which two-way frequency table correctly shows the marginal frequencies? A. 15 years old 16 years old Total ----------------------------------------------- 9th grade 2 0 2 10th grade 5 10 15 Total 10 10 17 B. 15 years old 16 years old Total ----------------------------------------------- 9th grade 2 0 2 10th grade 5 10 15 Total 7 10 17 C. 15 years old 16 years old Total ----------------------------------------------- 9th grade 2 0 2 10th grade 15 10 25 Total 17 10 27 D. 15 years old 16 years old Total ----------------------------------------------- 9th grade 2 0 2 10th grade 7 10 17 Total 9 10 19

The ages and grades of some of the 17 girls on a club soccer team are shown in the table. 15 years old 16 years old ------------------------------------- 9th grade 2 0 10th grade 10 Which two-way frequency table correctly shows the marginal frequencies? A. 15 years old 16 years old Total ----------------------------------------------- 9th grade 2 0 2 10th grade 5 10 15 Total 10 10 17 B. 15 years old 16 years old Total ----------------------------------------------- 9th grade 2 0 2 10th grade 5 10 15 Total 7 10 17 C. 15 years old 16 years old Total ----------------------------------------------- 9th grade 2 0 2 10th grade 15 10 25 Total 17 10 27 D. 15 years old 16 years old Total ----------------------------------------------- 9th grade 2 0 2 10th grade 7 10 17 Total 9 10 19
Transcript text: The ages and grades of some of the 17 girls on a club soccer team are shown in the table. \begin{tabular}{|c|c|c|} \hline & 15 years old & 16 years old \\ \hline 9 th grade & 2 & 0 \\ \hline 10 th grade & & 10 \\ \hline \end{tabular} Which two-way frequency table correctly shows the marginal frequencies? A. \begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} 15 years \\ old \end{tabular} & \begin{tabular}{c} 16 years \\ old \end{tabular} & Total \\ \hline 9 th grade & 2 & 0 & 2 \\ \hline 10 th grade & 5 & 10 & 15 \\ \hline Total & 10 & 10 & 17 \\ \hline \end{tabular} B. \begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} 15 years \\ old \end{tabular} & \begin{tabular}{c} 16 years \\ old \end{tabular} & Total \\ \hline 9h grade & 2 & 0 & 2 \\ \hline 10th grade & 5 & 10 & 15 \\ \hline Total & 7 & 10 & 17 \\ \hline \end{tabular} C. \begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} 15 years \\ old \end{tabular} & \begin{tabular}{c} 16 years \\ old \end{tabular} & Total \\ \hline $\mathbf{9} \mathrm{h}$ grade & 2 & 0 & 2 \\ \hline $\mathbf{1 0}$ th grade & 15 & 10 & 25 \\ \hline Total & 17 & 10 & 27 \\ \hline \end{tabular} D. \begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} 15 years \\ old \end{tabular} & \begin{tabular}{c} 16 years \\ old \end{tabular} & Total \\ \hline 9 th grade & 2 & 0 & 2 \\ \hline 10 th grade & 7 & 10 & 17 \\ \hline Total & 9 & 10 & 19 \\ \hline \end{tabular}
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Solution

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Solution Steps

To determine the correct two-way frequency table with marginal frequencies, we need to calculate the totals for each row and column based on the given data. The marginal frequencies are the sums of the rows and columns, which should add up to the total number of girls on the team, which is 17.

Step 1: Analyze the Given Data

The problem provides a table with the ages and grades of some of the 17 girls on a soccer team. The data is as follows:

  • 9th grade: 2 girls are 15 years old, 0 girls are 16 years old.
  • 10th grade: The number of 15-year-olds is unknown, and 10 girls are 16 years old.
Step 2: Calculate the Missing Value

To find the missing value for the number of 10th-grade girls who are 15 years old, we use the total number of girls: \[ \text{Total girls} = 17 \] The sum of known values is: \[ 2 \, (\text{9th grade, 15 years old}) + 0 \, (\text{9th grade, 16 years old}) + 10 \, (\text{10th grade, 16 years old}) = 12 \] Thus, the number of 10th-grade girls who are 15 years old is: \[ 17 - 12 = 5 \]

Step 3: Calculate Row Totals

The row totals are calculated as follows:

  • 9th grade total: \(2 + 0 = 2\)
  • 10th grade total: \(5 + 10 = 15\)
Step 4: Calculate Column Totals

The column totals are calculated as follows:

  • 15 years old total: \(2 + 5 = 7\)
  • 16 years old total: \(0 + 10 = 10\)
Step 5: Verify the Grand Total

The grand total is the sum of all individual entries, which should equal the total number of girls: \[ 2 + 0 + 5 + 10 = 17 \]

Final Answer

\(\boxed{\text{B}}\)

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