Find answers to your questions faster and easier with IDNLearn.com. Our Q&A platform offers reliable and thorough answers to ensure you have the information you need to succeed in any situation.
Sagot :
To determine the correct two-way frequency table with the marginal frequencies, we will go through the given data step by step.
Given:
- For 9th grade: 2 girls are 15 years old, 0 girls are 16 years old.
- For 10th grade: 10 girls are 16 years old.
We need to fill in the missing value for the 10th grade, 15 years old and calculate the marginal frequencies (totals).
### Step-by-step Calculation:
Step 1: Fill in the missing value for 10th grade, 15 years old.
- Given that the total number of girls is 17 and the sum of known values is [tex]\(2\)[/tex] (from 9th grade, 15 years old) + [tex]\(0\)[/tex] (from 9th grade, 16 years old) + [tex]\(10\)[/tex] (from 10th grade, 16 years old) = [tex]\(12\)[/tex].
- Therefore, the number of 15-year-old girls in 10th grade = [tex]\(17 - 12 = 5\)[/tex].
Now we have:
- 9th grade: 15 years old = 2, 16 years old = 0.
- 10th grade: 15 years old = 5, 16 years old = 10.
Step 2: Calculate the row and column totals (marginal frequencies).
- Row totals (grades):
- [tex]\(9\)[/tex]th grade total = [tex]\(2\)[/tex] (15 years old) + [tex]\(0\)[/tex] (16 years old) = [tex]\(2\)[/tex].
- [tex]\(10\)[/tex]th grade total = [tex]\(5\)[/tex] (15 years old) + [tex]\(10\)[/tex] (16 years old) = [tex]\(15\)[/tex].
- Column totals (ages):
- Total 15 years old = [tex]\(2\)[/tex] (9th grade) + [tex]\(5\)[/tex] (10th grade) = [tex]\(7\)[/tex].
- Total 16 years old = [tex]\(0\)[/tex] (9th grade) + [tex]\(10\)[/tex] (10th grade) = [tex]\(10\)[/tex].
- Grand total = [tex]\(9\)[/tex]th grade total + [tex]\(10\)[/tex]th grade total = [tex]\(2\)[/tex] + [tex]\(15\)[/tex] = [tex]\(17\)[/tex].
Step 3: Construct the two-way frequency table.
Given our calculations, the table should look like this:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & 15 \text{ years old} & 16 \text{ years old} & \text{Total} \\ \hline 9th grade & 2 & 0 & 2 \\ \hline 10th grade & 5 & 10 & 15 \\ \hline \text{Total} & 7 & 10 & 17 \\ \hline \end{tabular} \][/tex]
### Conclusion:
The correct two-way frequency table is Option A:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & 15 \text{ years old} & 16 \text{ years old} & \text{Total} \\ \hline 9th grade & 2 & 0 & 2 \\ \hline 10th grade & 5 & 10 & 15 \\ \hline \text{Total} & 7 & 10 & 17 \\ \hline \end{tabular} \][/tex]
Given:
- For 9th grade: 2 girls are 15 years old, 0 girls are 16 years old.
- For 10th grade: 10 girls are 16 years old.
We need to fill in the missing value for the 10th grade, 15 years old and calculate the marginal frequencies (totals).
### Step-by-step Calculation:
Step 1: Fill in the missing value for 10th grade, 15 years old.
- Given that the total number of girls is 17 and the sum of known values is [tex]\(2\)[/tex] (from 9th grade, 15 years old) + [tex]\(0\)[/tex] (from 9th grade, 16 years old) + [tex]\(10\)[/tex] (from 10th grade, 16 years old) = [tex]\(12\)[/tex].
- Therefore, the number of 15-year-old girls in 10th grade = [tex]\(17 - 12 = 5\)[/tex].
Now we have:
- 9th grade: 15 years old = 2, 16 years old = 0.
- 10th grade: 15 years old = 5, 16 years old = 10.
Step 2: Calculate the row and column totals (marginal frequencies).
- Row totals (grades):
- [tex]\(9\)[/tex]th grade total = [tex]\(2\)[/tex] (15 years old) + [tex]\(0\)[/tex] (16 years old) = [tex]\(2\)[/tex].
- [tex]\(10\)[/tex]th grade total = [tex]\(5\)[/tex] (15 years old) + [tex]\(10\)[/tex] (16 years old) = [tex]\(15\)[/tex].
- Column totals (ages):
- Total 15 years old = [tex]\(2\)[/tex] (9th grade) + [tex]\(5\)[/tex] (10th grade) = [tex]\(7\)[/tex].
- Total 16 years old = [tex]\(0\)[/tex] (9th grade) + [tex]\(10\)[/tex] (10th grade) = [tex]\(10\)[/tex].
- Grand total = [tex]\(9\)[/tex]th grade total + [tex]\(10\)[/tex]th grade total = [tex]\(2\)[/tex] + [tex]\(15\)[/tex] = [tex]\(17\)[/tex].
Step 3: Construct the two-way frequency table.
Given our calculations, the table should look like this:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & 15 \text{ years old} & 16 \text{ years old} & \text{Total} \\ \hline 9th grade & 2 & 0 & 2 \\ \hline 10th grade & 5 & 10 & 15 \\ \hline \text{Total} & 7 & 10 & 17 \\ \hline \end{tabular} \][/tex]
### Conclusion:
The correct two-way frequency table is Option A:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & 15 \text{ years old} & 16 \text{ years old} & \text{Total} \\ \hline 9th grade & 2 & 0 & 2 \\ \hline 10th grade & 5 & 10 & 15 \\ \hline \text{Total} & 7 & 10 & 17 \\ \hline \end{tabular} \][/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com is committed to providing accurate answers. Thanks for stopping by, and see you next time for more solutions.
