Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.