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Question 8 of 10

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

[tex]\[
\begin{tabular}{|c|c|c|}
\hline & $6 ^{\prime}$ or over & Under $6 ^{\prime}$ \\
\hline Male & 12 & 86 \\
\hline Female & 3 & 99 \\
\hline
\end{tabular}
\][/tex]

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

Sagot :

GinnyAnswer
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.
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