A survey of 180 students found that 72 students in the 10th grade prefer playing soccer. If the total number of students increases by 40, all new students being 10th graders who play soccer, the new marginal relative frequency of 10th-grade students is ________ (express as a fraction in simplest form).
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to calculate the marginal relative frequency after a change in the total population. The key is to understand how the addition of new students affects the marginal relative frequency.
Key Concept Explanation
Marginal Relative Frequency: It is the ratio of the marginal frequency (the number of students in a single variable category) to the total number of the population. In this case, it is the proportion of 10th-grade students among the total number of students.
Step-by-step Solution
1. Identify the initial marginal frequency of 10th-grade students: 72.
2. Determine the new total number of students: 180 + 40 = 220.
3. Calculate the new marginal frequency of 10th-grade students: 72 + 40 = 112.
4. Calculate the new marginal relative frequency:
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