To construct the correct two-way frequency table with marginal frequencies, we need to follow several steps:
1. Determine the given data and totals:
- Males 6' or over: 13
- Males under 6': 85
- Females 6' or over: 4
- Total adults: 200
2. Calculate the total number of males:
- Total males = Males 6' or over + Males under 6'
- Total males = 13 + 85 = 98
3. Determine the total number of females:
- Total females = Total adults - Total males
- Total females = 200 - 98 = 102
4. Calculate the number of females under 6':
- Females under 6' = Total females - Females 6' or over
- Females under 6' = 102 - 4 = 98
5. Calculate the totals for each height category:
- Total over 6' = Males 6' or over + Females 6' or over
- Total over 6' = 13 + 4 = 17
- Total under 6' = Males under 6' + Females under 6'
- Total under 6' = 85 + 98 = 183
6. Construct the two-way frequency table with marginal frequencies:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& $6 ^{\prime}$ or over & Under 6' & Total \\
\hline
Male & 13 & 85 & 98 \\
\hline
Female & 4 & 98 & 102 \\
\hline
Total & 17 & 183 & 200 \\
\hline
\end{tabular}
\][/tex]
Thus, the correct two-way frequency table shows the following marginal frequencies:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& $6 ^{\prime}$ or over & Under 6' & Total \\
\hline
Male & 13 & 85 & 98 \\
\hline
Female & 4 & 98 & 102 \\
\hline
Total & 17 & 183 & 200 \\
\hline
\end{tabular}
\][/tex]
This table accurately represents the given data and the calculated totals for each category and group.
