To determine the correct two-way frequency table showing the marginal frequencies, we need to complete the given table and fill in all the marginal totals.
The given partial table is:
\begin{tabular}{|l|c|c|}
\hline
& [tex]$6 ^{\prime}$[/tex] or over & Under [tex]$6^{\prime}$[/tex] \\
\hline
Male & 13 & 85 \\
\hline
Female & 4 & \\
\hline
\end{tabular}
From the total number of adults, we have 200 people in total.
1. Calculate the total number of males and females:
- The total number of males is the sum of males who are 6' or over and those under 6': \( 13 + 85 = 98 \).
- Therefore, the total number of females is \( 200 - 98 = 102 \).
2. Determine the number of females under 6':
- We already know there are 4 females who are 6' or over.
- Therefore, the number of females under 6' is \( 102 - 4 = 98 \).
3. Calculate the totals for each height category:
- People who are 6' or over: \( 13 (males) + 4 (females) = 17 \).
- People under 6': \( 85 (males) + 98 (females) = 183 \).
4. Verify the overall total:
- The total number of people: \( 17 (6' or over) + 183 (under 6') = 200 \).
Now, we can complete the two-way frequency table correctly:
\begin{tabular}{|l|c|c|c|}
\hline
& [tex]$6^{\prime}$[/tex] or over & Under [tex]$6^{\prime}$[/tex] & Total \\
\hline
Male & 13 & 85 & 98 \\
\hline
Female & 4 & 98 & 102 \\
\hline
Total & 17 & 183 & 200 \\
\hline
\end{tabular}
Thus, the correct answer is A.
