The heights of 200 adults were recorded and divided into two categories.

\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}

Which two-way frequency table correctly shows the marginal frequencies?

A.
\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}

B.
\begin{tabular}{|l|c|c|c|}
\hline & [tex]$6^{\prime}$[/tex] or over & Under 6' & Total \\
\hline Male & 13 & 85 & 98 \\
\hline Female & 4 & 115 & 119 \\
\hline Total & 17 & 200 & 217 \\
\hline
\end{tabular}

C.
\begin{tabular}{|l|c|c|c|}
\hline & [tex]$6^{\prime}$[/tex] or over & Under [tex]$6^{\prime}$[/tex] & Total \\
\hline Male & 13 & 85 & 100 \\
\hline Female & 4 & 96 & 100 \\
\hline Total & 17 & 181 & 200 \\
\hline
\end{tabular}

D.
\begin{tabular}{|l|c|c|c|}
\hline & [tex]$6^{\prime}$[/tex] or over & Under 6' & Total \\
\hline Male & 13 & 85 & 98 \\
\hline Female & 4 & 196 & 200 \\
\hline Total & 17 & 281 & 298 \\
\hline
\end{tabular}



Answer :

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.