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A sample of 50 11th graders were asked to select a favorite pattern out of 6 choices. The data 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 purple bar?



Answer :

GinnyAnswer
To determine the height of the purple bar in a relative frequency bar graph, you need to convert the given frequency for the purple color pattern into a relative frequency (percentage).

First, let's review the data provided:

- Total number of students surveyed = 5011
- Frequency of students who chose purple = 11

Next, let's calculate the relative frequency of students who chose the purple color pattern. The relative frequency is given by the formula:

[tex]\[ \text{Relative frequency} = \left( \frac{\text{Frequency of the color pattern}}{\text{Total number of students}} \right) \times 100 \][/tex]

Using the values given:

[tex]\[ \text{Relative frequency of purple} = \left( \frac{11}{5011} \right) \times 100 \][/tex]

Based on the given data, this relative frequency calculates to approximately [tex]\( 0.2195 \% \)[/tex].

So, the height of the purple bar on a relative frequency bar graph, where the vertical axis is marked in percentages, will be about [tex]\( 0.2195 \% \)[/tex].

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