To construct the correct two-way frequency table with marginal frequencies for the given problem, let's go through the information step-by-step:
1. Given Data:
- The number of males who are 6' or over: 12
- The number of males who are under 6': 86
- The number of females who are 6' or over: 3
2. Total Number of Adults:
- We know the total number of adults is 200.
3. Calculate the Total Number of Males:
- Total number of males = Males 6' or over + Males under 6'
- Total number of males = 12 + 86 = 98
4. Calculate the Total Number of Females:
- Total number of females = Total number of adults - Total number of males
- Total number of females = 200 - 98 = 102
5. Calculate the Number of Females Under 6':
- Total number of females under 6' = Total number of females - Females 6' or over
- Total number of females under 6' = 102 - 3 = 99
6. Calculate the Total Number of Adults 6' or Over:
- Total number of adults 6' or over = Males 6' or over + Females 6' or over
- Total number of adults 6' or over = 12 + 3 = 15
7. Calculate the Total Number of Adults Under 6':
- Total number of adults under 6' = Males under 6' + Females under 6'
- Total number of adults under 6' = 86 + 99 = 185
Now, we can construct the two-way frequency table with the marginal frequencies included:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& $6 ^{\prime}$ or over & Under $6 ^{\prime}$ & Total \\
\hline
Male & 12 & 86 & 98 \\
\hline
Female & 3 & 99 & 102 \\
\hline
Total & 15 & 185 & 200 \\
\hline
\end{tabular}
\][/tex]
This table accurately represents the marginal frequencies as well as the given data for the problem.
