Answer :
Let's carefully analyze the information provided and the results to determine which table correctly compares the measures of center (Medians) and the measures of variability (Ranges and Interquartile Ranges).
We have three tables to compare.
### Table 1
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & Median & Range & Interquartile Range \\ \hline Spanish & 85 & 40 & 25 \\ \hline French & 80 & 35 & 15 \\ \hline & \begin{tabular}{l} Difference \\ in Medians: \\ 5 \end{tabular} & \begin{tabular}{l} Difference \\ in Ranges: \\ 5 \end{tabular} & \begin{tabular}{l} Difference in \\ Interquartile Ranges: \\ 10 \end{tabular} \\ \hline \end{tabular} \][/tex]
### Table 2
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & Median & Range & Interquartile Range \\ \hline Spanish & 85 & 25 & 40 \\ \hline French & 80 & 15 & 35 \\ \hline & \begin{tabular}{l} Difference \\ in Medians: \\ 5 \end{tabular} & \begin{tabular}{l} Difference \\ in Ranges: \\ 10 \end{tabular} & \begin{tabular}{l} Difference in \\ Interquartile Ranges: \\ 5 \end{tabular} \\ \hline \end{tabular} \][/tex]
### Table 3
[tex]\[ \begin{tabular}{|c|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Median & Range & Interquartile Range \\ \hline Spanish & 70 & 25 & 40 \\ \hline French & 75 & 15 & 35 \\ \hline & \begin{tabular}{l} Difference \\ in Medians: \\ -5 \end{tabular} & \begin{tabular}{l} Difference \\ in Ranges: \\ 10 \end{tabular} & \begin{tabular}{l} Difference in \\ Interquartile Ranges: \\ 5 \end{tabular} \\ \hline \end{tabular} \][/tex]
Based on the calculations from the provided data:
1. Table 1:
- The difference in Medians is [tex]\(85 - 80 = 5\)[/tex].
- The difference in Ranges is [tex]\(40 - 35 = 5\)[/tex].
- The difference in Interquartile Ranges is [tex]\(25 - 15 = 10\)[/tex].
2. Table 2:
- The difference in Medians is [tex]\(85 - 80 = 5\)[/tex].
- The difference in Ranges is [tex]\(25 - 15 = 10\)[/tex].
- The difference in Interquartile Ranges is [tex]\(40 - 35 = 5\)[/tex].
3. Table 3:
- The difference in Medians is [tex]\(70 - 75 = -5\)[/tex].
- The difference in Ranges is [tex]\(25 - 15 = 10\)[/tex].
- The difference in Interquartile Ranges is [tex]\(40 - 35 = 5\)[/tex].
Comparing these calculations with the results provided:
- Table 1 results: {'Difference in Medians': 5, 'Difference in Ranges': 5, 'Difference in IQRs': 10}
- Table 2 results: {'Difference in Medians': 5, 'Difference in Ranges': 10, 'Difference in IQRs': 5}
- Table 3 results: {'Difference in Medians': -5, 'Difference in Ranges': 10, 'Difference in IQRs': 5}
From the observed values, all three tables match correctly with the respective differences in the measures of center and the measures of variability as calculated.
Thus, all three tables correctly compare the measures of center and the measures of variability.
We have three tables to compare.
### Table 1
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & Median & Range & Interquartile Range \\ \hline Spanish & 85 & 40 & 25 \\ \hline French & 80 & 35 & 15 \\ \hline & \begin{tabular}{l} Difference \\ in Medians: \\ 5 \end{tabular} & \begin{tabular}{l} Difference \\ in Ranges: \\ 5 \end{tabular} & \begin{tabular}{l} Difference in \\ Interquartile Ranges: \\ 10 \end{tabular} \\ \hline \end{tabular} \][/tex]
### Table 2
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & Median & Range & Interquartile Range \\ \hline Spanish & 85 & 25 & 40 \\ \hline French & 80 & 15 & 35 \\ \hline & \begin{tabular}{l} Difference \\ in Medians: \\ 5 \end{tabular} & \begin{tabular}{l} Difference \\ in Ranges: \\ 10 \end{tabular} & \begin{tabular}{l} Difference in \\ Interquartile Ranges: \\ 5 \end{tabular} \\ \hline \end{tabular} \][/tex]
### Table 3
[tex]\[ \begin{tabular}{|c|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Median & Range & Interquartile Range \\ \hline Spanish & 70 & 25 & 40 \\ \hline French & 75 & 15 & 35 \\ \hline & \begin{tabular}{l} Difference \\ in Medians: \\ -5 \end{tabular} & \begin{tabular}{l} Difference \\ in Ranges: \\ 10 \end{tabular} & \begin{tabular}{l} Difference in \\ Interquartile Ranges: \\ 5 \end{tabular} \\ \hline \end{tabular} \][/tex]
Based on the calculations from the provided data:
1. Table 1:
- The difference in Medians is [tex]\(85 - 80 = 5\)[/tex].
- The difference in Ranges is [tex]\(40 - 35 = 5\)[/tex].
- The difference in Interquartile Ranges is [tex]\(25 - 15 = 10\)[/tex].
2. Table 2:
- The difference in Medians is [tex]\(85 - 80 = 5\)[/tex].
- The difference in Ranges is [tex]\(25 - 15 = 10\)[/tex].
- The difference in Interquartile Ranges is [tex]\(40 - 35 = 5\)[/tex].
3. Table 3:
- The difference in Medians is [tex]\(70 - 75 = -5\)[/tex].
- The difference in Ranges is [tex]\(25 - 15 = 10\)[/tex].
- The difference in Interquartile Ranges is [tex]\(40 - 35 = 5\)[/tex].
Comparing these calculations with the results provided:
- Table 1 results: {'Difference in Medians': 5, 'Difference in Ranges': 5, 'Difference in IQRs': 10}
- Table 2 results: {'Difference in Medians': 5, 'Difference in Ranges': 10, 'Difference in IQRs': 5}
- Table 3 results: {'Difference in Medians': -5, 'Difference in Ranges': 10, 'Difference in IQRs': 5}
From the observed values, all three tables match correctly with the respective differences in the measures of center and the measures of variability as calculated.
Thus, all three tables correctly compare the measures of center and the measures of variability.
