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A sample of 50 eleventh 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 & 3 \\
\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?



Answer :

GinnyAnswer
To determine the height of the green bar in a relative frequency bar graph, we need to convert the given frequency of the green pattern into a percentage relative to the total number of students surveyed.

Here’s the step-by-step process:

1. Identify the total number of students surveyed:
- Total number of students: [tex]\( 5011 \)[/tex]

2. Identify the frequency of the green bar:
- Frequency of the green pattern: [tex]\( 9 \)[/tex]

3. Calculate the relative frequency of the green pattern:
- This relative frequency is expressed as the percentage of students who identified green as their favorite pattern.
- The formula for relative frequency is [tex]\(\left(\frac{\text{Frequency}}{\text{Total number of students}}\right) \times 100\)[/tex]

4. Plug in the values:
[tex]\[ \left(\frac{9}{5011}\right) \times 100 \approx 0.1796\% \][/tex]

Therefore, the height of the green bar, when represented as a relative frequency in the bar graph, will be approximately [tex]\(0.1796\%\)[/tex].

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