Let's solve this step-by-step based on the information provided:
1. Identify the given data:
- Number of males 6 feet or over: 14
- Number of males under 6 feet: 88
- Number of females 6 feet or over: 2
- Total number of individuals: 200
2. Calculate the number of females under 6 feet:
We start by determining how many females are under 6 feet.
[tex]\[
\text{Total females under 6 feet} = \text{Total individuals} - (\text{Males 6 or over} + \text{Males under 6} + \text{Females 6 or over})
\][/tex]
[tex]\[
\text{Total females under 6 feet} = 200 - (14 + 88 + 2) = 200 - 104 = 96
\][/tex]
3. Calculate the marginal totals for each category (gender and height):
- Total number of individuals 6 feet or over:
[tex]\[
\text{Total 6 or over} = \text{Males 6 or over} + \text{Females 6 or over} = 14 + 2 = 16
\][/tex]
- Total number of individuals under 6 feet:
[tex]\[
\text{Total under 6} = \text{Males under 6} + \text{Females under 6} = 88 + 96 = 184
\][/tex]
- Total number of males:
[tex]\[
\text{Total males} = \text{Males 6 or over} + \text{Males under 6} = 14 + 88 = 102
\][/tex]
- Total number of females:
[tex]\[
\text{Total females} = \text{Females 6 or over} + \text{Females under 6} = 2 + 96 = 98
\][/tex]
4. Construct the frequency table based on these totals:
Checking with the provided options given:
Option A:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \begin{tabular}{l}
$6^{\prime}$ or \\
over
\end{tabular} & \begin{tabular}{c}
Under \\
$6^{\prime}$
\end{tabular} & Total \\
\hline Male & 14 & 88 & 102 \\
\hline Female & 2 & 96 & 98 \\
\hline Total & 16 & 184 & 200 \\
\hline
\end{tabular}
\][/tex]
This matches our calculated values perfectly. Let's verify that the other options do not match:
Option B:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \begin{tabular}{c}
$6^{\prime}$ or \\
over
\end{tabular} & \begin{tabular}{c}
Under \\
$6^{\prime}$
\end{tabular} & Total \\
\hline Male & 14 & 88 & 112 \\
\hline Female & 2 & 94 & 104 \\
\hline Total & 16 & 200 & 216 \\
\hline
\end{tabular}
\][/tex]
The totals do not match our calculations.
Option C:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \begin{tabular}{c}
$6^{\prime}$ or \\
over
\end{tabular} & \begin{tabular}{c}
Under \\
$6^{\prime}$
\end{tabular} & Total \\
\hline Male & 14 & 88 & 102 \\
\hline Female & 2 & 198 & 200 \\
\hline Total & 16 & 286 & 302 \\
\hline
\end{tabular}
\][/tex]
The totals do not match our calculations either.
Therefore, the correct frequency table is:
Option A:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \begin{tabular}{l}
$6^{\prime}$ or \\
over
\end{tabular} & \begin{tabular}{c}
Under \\
$6^{\prime}$
\end{tabular} & Total \\
\hline Male & 14 & 88 & 102 \\
\hline Female & 2 & 96 & 98 \\
\hline Total & 16 & 184 & 200 \\
\hline
\end{tabular}
\][/tex]
