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A sample of 501 11th graders were asked to select a favorite pattern out of 6 choices. The data list below shows what their favorite color patterns were, and the accompanying frequency table and bar graph represent these data. In the bar graph, the height of the blue-gray bar is 4, the height of the green bar is 9, and so on.

\begin{tabular}{|c|c|}
\hline
Color Pattern & Frequency \\
\hline
Blue on gray & 4 \\
\hline
Green & 9 \\
\hline
Pink polka dots & 14 \\
\hline
Purple & 11 \\
\hline
Red and orange stripes & 9 \\
\hline
Yellow & 9 \\
\hline
\end{tabular}

Suppose that, rather than being just a bar graph, the display you see above is a relative frequency bar graph. The vertical axis of the graph will be marked off in percentages, from 0 percent up to 30 percent. What will be the height of the green bar?

A. 18

B. 25

C. 15

D. 9



Answer :

GinnyAnswer
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.

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