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.
| | 7th | 8th | Total |
| :---- | :---- | :---- | :------ |
| Drama | 11 % | 15 % | 26 % |
| Action | 25 % | 19 % | 44 % |
| Comedy | 14 % | 16 % | 30 % |
| Total | 50 % | 50 % | 100 % |
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 16[tex]$\%$[/tex].
D. Most students prefer drama movies.
E. Half or the 7th graders prefer action movies.
Answer (1)
The marginal relative frequency for action movies is 44% .
The joint relative frequency for 8th graders who like comedy movies is 16% .
Explanation
Analyze the problem and data We start by analyzing the given two-way table, which shows the movie preferences of 7th and 8th graders. The table provides percentages representing relative frequencies. Our goal is to determine which of the given statements are correct based on the data in the table.
Evaluate statement 1 Statement 1: "More 7th graders were surveyed than 8th graders." The table shows that 7th graders represent 50% of the total and 8th graders also represent 50% of the total. This means the number of students surveyed in each grade is the same. Therefore, this statement is incorrect.
Evaluate statement 2 Statement 2: "The marginal relative frequency for action movies is 44%." The table shows that the total percentage for action movies is 44%. Therefore, this statement is correct.
Evaluate statement 3 Statement 3: "The joint relative frequency for 8th graders who like comedy movies is 16%." The table shows that 16% of the students are 8th graders who like comedy movies. Therefore, this statement is correct.
Evaluate statement 4 Statement 4: "Most students prefer drama movies." The percentages for Drama, Action, and Comedy are 26%, 44%, and 30% respectively. Since 44% > 30% > 26%, most students prefer action movies, not drama movies. Therefore, this statement is incorrect.
Evaluate statement 5 Statement 5: "Half or the 7th graders preter action movies." The table shows that 25% of the students are 7th graders who like action movies. Since 25% is not half of the 7th graders (50%), this statement is incorrect.
Final Answer Based on our analysis, 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%.
Examples
Understanding movie preferences among different age groups can help movie studios tailor their marketing strategies. For example, if a studio knows that a large percentage of 8th graders enjoy comedies, they might focus their advertising efforts for a new comedy film towards that demographic. Similarly, knowing the overall popularity of action movies can inform decisions about which genres to invest in. This type of analysis is also useful for streaming services when recommending content to users.
