To answer this question, we will use the concept of relative frequency to convert the given frequency of the green pattern to a percentage and then determine the height of the green bar on the relative frequency bar graph.
First, let's break down the given information and the required steps in detail:
1. Total number of students: The total number of students surveyed is 5011.
2. Frequency of the green pattern: The frequency (or the number of students who chose the green pattern) is 9.
3. Calculate the relative frequency: The relative frequency of the green pattern is found by taking the frequency of the green pattern and dividing it by the total number of students. This result is then converted to a percentage by multiplying by 100.
[tex]\[
\text{Relative frequency of green} = \left( \frac{\text{Frequency of green}}{\text{Total number of students}} \right) \times 100
\][/tex]
Plugging in the values, we get:
[tex]\[
\text{Relative frequency of green} = \left( \frac{9}{5011} \right) \times 100 \approx 0.1796\%
\][/tex]
4. Determine the height of the green bar on a relative frequency bar graph: The vertical axis of the bar graph is marked from 0% to 30%, and we need to map the relative frequency percentage to this axis. Given the axis is 30% tall, we calculate the actual height of the bar in the graph by using the relative frequency percentage we found earlier:
[tex]\[
\text{Height of green bar in graph} = \left( \frac{\text{Relative frequency of green}}{100} \right) \times 30
\][/tex]
Plugging in the relative frequency:
[tex]\[
\text{Height of green bar in graph} = \left( \frac{0.1796}{100} \right) \times 30 \approx 0.05388
\][/tex]
Rounding this to the nearest whole number, we get:
[tex]\[
\text{Height of green bar in graph} \approx 0
\][/tex]
Therefore, in a relative frequency bar graph where the vertical axis is marked off from 0% to 30%, the height of the green bar would be approximately 0 units tall, which is closest to option C. However, none of the provided options (18, 25, 9, 15) seem to align with this calculation given. This discrepancy suggests a potential error in the provided options.
Without correcting the problem in the setup or with more specific contextual information, the calculation stands as described. The most accurate portrayal based on the given data would be a height very close to zero.
