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

\begin{tabular}{|c|c|c|}
\hline
& Over & Under \\
\hline
Male & 13 & 85 \\
\hline
Female & 4 & 98 \\
\hline
\end{tabular}

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

A.
\begin{tabular}{|c|c|c|c|}
\hline
& Over & Under & Total \\
\hline
Male & 13 & 85 & 98 \\
\hline
Female & 4 & 98 & 102 \\
\hline
Total & 17 & 183 & 200 \\
\hline
\end{tabular}

B.
\begin{tabular}{|c|c|c|c|}
\hline
& Over & Under & Total \\
\hline
Male & 13 & 85 & 98 \\
\hline
Female & 4 & 196 & 200 \\
\hline
Total & 17 & 281 & 298 \\
\hline
\end{tabular}

C.
\begin{tabular}{|c|c|c|c|}
\hline
& Over & Under & Total \\
\hline
Male & 13 & 85 & 98 \\
\hline
Female & 4 & 115 & 119 \\
\hline
Total & 17 & 200 & 217 \\
\hline
\end{tabular}

D.
\begin{tabular}{|c|c|c|c|}
\hline
& Over & Under & Total \\
\hline
Male & 13 & 35 & 48 \\
\hline
Female & 4 & 38 & 42 \\
\hline
Total & 17 & 73 & 90 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To determine which two-way frequency table correctly shows the marginal frequencies for the given data, we need to consider the totals for each category. First, let’s summarize the given information:

- For males:
- Over 6: 13
- Under 6: 85

- For females:
- Over 6: 4
- Under 6: 98

Next, let's calculate the marginal frequencies:

1. Total Over 6:
- Sum of males over 6 and females over 6:
[tex]\[ 13 + 4 = 17 \][/tex]

2. Total Under 6:
- Sum of males under 6 and females under 6:
[tex]\[ 85 + 98 = 183 \][/tex]

3. Total Males:
- Sum of males over 6 and under 6:
[tex]\[ 13 + 85 = 98 \][/tex]

4. Total Females:
- Sum of females over 6 and under 6:
[tex]\[ 4 + 98 = 102 \][/tex]

5. Grand Total:
- Sum of all entries:
[tex]\[ 17 + 183 = 200 \][/tex]

Now let’s look at the given options and determine which one matches our calculated results:

### Option A
\begin{tabular}{|c|c|c|c|}
\hline
& Over 6 & Under 6 & Total \\
\hline
Male & 13 & 85 & 98 \\
\hline
Female & 4 & 98 & 102 \\
\hline
Total & 17 & 183 & 200 \\
\hline
\end{tabular}

- This option correctly sums the data and marginal frequencies. Total values match our calculations.

### Option B
\begin{tabular}{|c|c|c|c|}
\hline
& Over 6 & Under 6 & Total \\
\hline
Male & 13 & 85 & 98 \\
\hline
Female & 4 & 196 & 200 \\
\hline
Total & 17 & 281 & 298 \\
\hline
\end{tabular}

- Clearly incorrect, as the figures do not align with our calculations.

### Option C
\begin{tabular}{|c|c|c|c|}
\hline
& Over 6 & Under 6 & Total \\
\hline
Male & 13 & 85 & 98 \\
\hline
Female & 4 & 115 & 119 \\
\hline
Total & 17 & 200 & 217 \\
\hline
\end{tabular}

- This option is also incorrect given the sums do not match our calculated totals.

### Option D
\begin{tabular}{|c|c|c|c|}
\hline
& Over 6 & Under 6 & Total \\
\hline
Male & 13 & 85 & 98 \\
\hline
Female & 4 & 38 & 42 \\
\hline
Total & 17 & 123 & 140 \\
\hline
\end{tabular}

- This option once again doesn’t align with our derived totals.

Hence, the correct two-way frequency table is:

### Option A
\begin{tabular}{|c|c|c|c|}
\hline
& Over 6 & Under 6 & Total \\
\hline
Male & 13 & 85 & 98 \\
\hline
Female & 4 & 98 & 102 \\
\hline
Total & 17 & 183 & 200 \\
\hline
\end{tabular}

This table accurately reflects the marginal frequencies obtained from our given data.
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