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The guidance office at a high school surveyed their [tex]$12^{\text{th}}$[/tex] grade students to determine in which of four states they would prefer to live after high school. The results are summarized in the two-way frequency table below.

\begin{tabular}{|c|c|c|c|c|c|}
\cline{2-6}
\multicolumn{1}{c|}{} & CA & TX & NY & FL & Total \\
\hline
Boys & 84 & 38 & 64 & 44 & 230 \\
\hline
Girls & 50 & 44 & 26 & 50 & 170 \\
\hline
Total & 134 & 82 & 90 & 94 & 400 \\
\hline
\end{tabular}

Which two-way table accurately represents the relative frequency for the whole table in this situation?

A.
\begin{tabular}{|c|c|c|c|c|c|}
\cline{2-6}
\multicolumn{1}{c|}{} & CA & TX & NY & FL & Total \\
\hline
Boys & 0.627 & 0.463 & 0.711 & 0.468 & 0.575 \\
\hline
Girls & 0.373 & 0.537 & 0.289 & 0.532 & 0.425 \\
\hline
Total & 1 & 1 & 1 & 1 & 1 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let's analyze the given data to find the relative frequencies for the whole table.

Here is the summarized two-way frequency table with absolute numbers:
\begin{tabular}{|c|c|c|c|c|c|}
\cline { 2 - 5 } \multicolumn{1}{c|}{} & CA & TX & NY & FL & Total \\
\hline Boys & 84 & 38 & 64 & 44 & 230 \\
\hline Girls & 50 & 44 & 26 & 50 & 170 \\
\hline Total & 134 & 82 & 90 & 94 & 400 \\
\hline
\end{tabular}

To convert these into relative frequencies, we use the totals for boys (230), girls (170), and overall students (400). Here are the relative frequencies provided from the answer:

Relative Frequencies for Boys:
- CA: 0.3652173913043478
- TX: 0.16521739130434782
- NY: 0.2782608695652174
- FL: 0.19130434782608696
- Total: 0.575

Relative Frequencies for Girls:
- CA: 0.29411764705882354
- TX: 0.25882352941176473
- NY: 0.15294117647058825
- FL: 0.29411764705882354
- Total: 0.425

Relative Frequencies for Total:
- CA: 0.335
- TX: 0.205
- NY: 0.225
- FL: 0.235
- Total: 1.0

Now, we can put these values back into the two-way table format:

\begin{tabular}{|c|c|c|c|c|c|}
\cline { 2 - 6 } \multicolumn{1}{c|}{} & CA & TX & NY & FL & Total \\
\hline Boys & 0.365 & 0.165 & 0.278 & 0.191 & 0.575 \\
\hline Girls & 0.294 & 0.259 & 0.153 & 0.294 & 0.425 \\
\hline Total & 0.335 & 0.205 & 0.225 & 0.235 & 1.000 \\
\hline
\end{tabular}

Upon evaluating the multiple-choice options, it is clear that none of these options match the calculated relative frequency table. The correct calculations are as tabulated above, and option A does not represent the correct relative frequencies.

Thus, none of the given options (including A) accurately represents the relative frequency for the whole table in this situation.

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