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Answer :
To determine the height of the green bar when the vertical axis is marked off in percentages up to 30%, follow these steps:
1. Find the total number of 11th graders sampled: The total number of 11th graders sampled is given as 5011.
2. Determine the frequency of selecting the green pattern: The frequency of selecting the green pattern is provided as 9.
3. Calculate the relative frequency (percentage) of students selecting the green pattern:
[tex]\[
\text{Relative frequency (percentage)} = \left( \frac{\text{Frequency of green pattern}}{\text{Total number of students sampled}} \right) \times 100
\][/tex]
Substituting the given values:
[tex]\[
\left( \frac{9}{5011} \right) \times 100 \approx 0.1796\%
\][/tex]
So, approximately 0.1796% of the students selected the green pattern.
4. Adjust the relative frequency to fit the vertical axis marked in percentages (up to 30%): The question states that the vertical axis goes up to 30%. To find the adjusted height of the green bar:
[tex]\[
\text{Height of the green bar} = \frac{\text{Green percentage}}{30\%} \times 100\%
\][/tex]
Using the calculated percentage:
[tex]\[
\frac{0.1796\%}{30\%} \times 100\% \approx 0.5987
\][/tex]
Therefore, the height of the green bar in the relative frequency bar graph is approximately 0.5987. As per the options provided:
A. 18
B. 25
C. 15
D. 9
None of these options directly match the calculated height. Considering the closest approximation:
Thus, we conclude that the closest anticipated value would align with none of the provided choices. However, based on traditional problem-setting, it's plausible an error or approximations are involved, and thus no absolute match here aligns with given choices directly.
1. Find the total number of 11th graders sampled: The total number of 11th graders sampled is given as 5011.
2. Determine the frequency of selecting the green pattern: The frequency of selecting the green pattern is provided as 9.
3. Calculate the relative frequency (percentage) of students selecting the green pattern:
[tex]\[
\text{Relative frequency (percentage)} = \left( \frac{\text{Frequency of green pattern}}{\text{Total number of students sampled}} \right) \times 100
\][/tex]
Substituting the given values:
[tex]\[
\left( \frac{9}{5011} \right) \times 100 \approx 0.1796\%
\][/tex]
So, approximately 0.1796% of the students selected the green pattern.
4. Adjust the relative frequency to fit the vertical axis marked in percentages (up to 30%): The question states that the vertical axis goes up to 30%. To find the adjusted height of the green bar:
[tex]\[
\text{Height of the green bar} = \frac{\text{Green percentage}}{30\%} \times 100\%
\][/tex]
Using the calculated percentage:
[tex]\[
\frac{0.1796\%}{30\%} \times 100\% \approx 0.5987
\][/tex]
Therefore, the height of the green bar in the relative frequency bar graph is approximately 0.5987. As per the options provided:
A. 18
B. 25
C. 15
D. 9
None of these options directly match the calculated height. Considering the closest approximation:
Thus, we conclude that the closest anticipated value would align with none of the provided choices. However, based on traditional problem-setting, it's plausible an error or approximations are involved, and thus no absolute match here aligns with given choices directly.
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