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A sample of 50 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
\begin{tabular}{c}
Red and orange stripes
\end{tabular} & 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 yellow bar?

A. 3
B. 4
C. 6
D. 9



Answer :

GinnyAnswer
To solve this problem, let's go through the process step-by-step to determine the height of the yellow bar in a relative frequency bar graph.

1. Understand the data and calculate the relative frequency:
- Total number of students surveyed: [tex]\(5011\)[/tex]
- Number of students who selected yellow: [tex]\(3\)[/tex]

2. Calculate the relative frequency (percentage) for the yellow bar:
- The relative frequency is found by dividing the number of students who selected yellow by the total number of students and then multiplying by 100 to convert it to a percentage.

[tex]\[ \text{Relative Frequency (percentage)} = \left( \frac{3}{5011} \right) \times 100 \][/tex]

3. Convert the relative frequency to percentage:

[tex]\[ \text{Relative Frequency (percentage)} = 0.059868289762522446 \][/tex]

4. Round the relative frequency to the nearest whole number:

- The relative frequency of [tex]\(0.059868289762522446\)[/tex] when rounded to the nearest whole number is [tex]\(0\)[/tex].

Therefore, the height of the yellow bar in the relative frequency bar graph will be [tex]\(\boxed{0}\)[/tex].

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