- The marginal frequency is found by summing the values in the 'Computer Games' column for both grades.
- Identify the number of 11th grade students who prefer computer games: \(4\).
- Identify the number of 12th grade students who prefer computer games: \(15\).
- Sum these values to get the total marginal frequency: \(4 + 15 = \boxed{19}\).
Explanation
- Understand the goal and definitions
We start by examining the provided contingency table, which categorizes students by their grade level (11th or 12th) and their preferred leisure time activity (Computer Games, Music, or Watching movies/TV). The marginal frequency of a category represents the total number of students who fall into that category, regardless of other variables—in this case, their grade. To find the marginal frequency of students who prefer playing computer games, we need to sum the number of 11th grade students who prefer computer games and the number of 12th grade students who prefer computer games.
- Calculate the marginal frequency
From the table, we can identify the following values:
- Number of 11th grade students who prefer computer games: \(4\)
- Number of 12th grade students who prefer computer games: \(15\)
The marginal frequency for 'Computer Games' is the total count of students who chose this activity across both grade levels. We calculate this by adding the values from the two rows for the 'Computer Games' column:
\[\text{Marginal Frequency (Computer Games)} = 4 + 15\]
\[\text{Marginal Frequency (Computer Games)} = 19\]
- Conclusion and final check
We have determined that the marginal frequency for students who prefer computer games is \(19\). This value represents the total number of survey participants across both grades who indicated that playing computer games is their favorite free-time activity. Comparing our result to the given options, we confirm that \(19\) is the correct choice.
Examples
Understanding marginal frequencies is essential in data analysis, particularly when interpreting survey results. For instance, if you were managing a school's recreation budget, knowing that \(19\) out of \(80\) students prefer computer games helps you allocate resources effectively, such as purchasing gaming consoles for the student lounge. This same process can be applied to any contingency table to quickly identify the overall preference or frequency of a specific subset of data.