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Interpreting a Relative Frequency Table

Students in 7th and 8th grade were asked the types of movies they prefer. The results of the survey are shown in the two-way table.

\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & 7th & 8th & Total \\
\hline Drama & [tex]$11 \%$[/tex] & [tex]$15 \%$[/tex] & [tex]$26 \%$[/tex] \\
\hline Action & [tex]$25 \%$[/tex] & [tex]$19 \%$[/tex] & [tex]$44 \%$[/tex] \\
\hline Comedy & [tex]$14 \%$[/tex] & [tex]$16 \%$[/tex] & [tex]$30 \%$[/tex] \\
\hline Total & [tex]$50 \%$[/tex] & [tex]$50 \%$[/tex] & [tex]$100 \%$[/tex] \\
\hline
\end{tabular}

Which statements are correct? Check all that apply.

A. More 7th graders were surveyed than 8th graders.
B. The marginal relative frequency for action movies is [tex]$44 \%$[/tex].
C. The joint relative frequency for 8th graders who like comedy movies is [tex]$16 \%$[/tex].
D. Most students prefer drama movies.
E. Half of the 7th graders prefer action movies.

Sagot :

GinnyAnswer
To analyze the relative frequency table and check which statements are correct, let's break down each statement step-by-step:

1. More 7th graders were surveyed than 8th graders.
- According to the table, the total percentage of 7th graders surveyed is 50%, and the total percentage of 8th graders surveyed is also 50%.
- Since the percentages are equal, it means that an equal number of 7th and 8th graders were surveyed.
- Therefore, this statement is False.

2. The marginal relative frequency for action movies is 44%.
- The marginal relative frequency is the total percentage of students who prefer action movies, regardless of their grade.
- According to the table, the total percentage for action movies is 44%.
- Therefore, this statement is True.

3. The joint relative frequency for 8th graders who like comedy movies is 16%.
- Joint relative frequency refers to the percentage of a specific subgroup—in this case, 8th graders who like comedy movies.
- According to the table, 16% of 8th graders prefer comedy movies.
- Therefore, this statement is True.

4. Most students prefer drama movies.
- To determine if most students prefer drama movies, we need to compare it to the other movie preferences.
- According to the table, 26% of students prefer drama movies, 44% prefer action movies, and 30% prefer comedy movies.
- Since 26% is not the highest percentage, drama is not the most preferred genre.
- Therefore, this statement is False.

5. Half of the 7th graders prefer action movies.
- We need to check the percentage of 7th graders who prefer action movies.
- According to the table, 25% of 7th graders prefer action movies.
- Therefore, it is not correct to say that half (50%) of the 7th graders prefer action movies.
- Therefore, this statement is False.

So, the correct statements are:
- The marginal relative frequency for action movies is 44%.
- The joint relative frequency for 8th graders who like comedy movies is 16%.
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