High School

A sample of 50 eleventh graders was 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.

[tex]
\[
\begin{tabular}{|c|c|}
\hline
Color Pattern & Frequency \\
\hline
Blue on gray & 4 \\
\hline
Green & 9 \\
\hline
Pink polka dots & 14 \\
\hline
Purple & 11 \\
\hline
\begin{tabular}{c}
Red and orange \\
stripes
\end{tabular} & 9 \\
\hline
Yellow & 3 \\
\hline
\end{tabular}
\]
[/tex]

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. 9
C. 15
D. 25

Answer :

To determine the height of the green bar in a relative frequency bar graph, we need to calculate the percentage of students who chose the green pattern as their favorite.

1. Understand the Total Sample Size:
- The sample size consists of 50 students, as indicated by the data.

2. Frequency of the Green Pattern:
- According to the table, the frequency of students who preferred the green pattern is 9.

3. Calculate the Relative Frequency:
- Relative frequency as a percentage is calculated by dividing the frequency of the category (green) by the total sample size and then multiplying by 100 to convert it into a percentage.

[tex]\[
\text{Relative Frequency (\%)} = \left( \frac{\text{Frequency of Green}}{\text{Total Sample Size}} \right) \times 100
\][/tex]

[tex]\[
\text{Relative Frequency (\%)} = \left( \frac{9}{50} \right) \times 100 = 18\%
\][/tex]

4. Interpret the Result:
- The calculated relative frequency for the green bar is 18%. Therefore, on the relative frequency bar graph, the height of the green bar would represent 18%.

5. Select the Correct Option:
- Out of the options provided (A. 18, B. 9, C. 15, D. 25), the correct height for the green bar is 18.

Therefore, the height of the green bar is 18%, so the answer is A. 18.