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%.
