Let's go through the steps needed to generate the frequency table and find the relative frequency for the range [tex]\(11-15\)[/tex].
1. List the data and ranges: We are given the data:
[tex]\[3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19\][/tex]
We need to count the number of values that fall into each of the specified ranges.
2. Count the values in each range:
- Range [tex]\(1-5\)[/tex]: Values in range: [tex]\(3, 2, 3\)[/tex]
[tex]\[
\text{Number of Values: } 3
\][/tex]
- Range [tex]\(6-10\)[/tex]: Values in range: [tex]\(6\)[/tex]
[tex]\[
\text{Number of Values: } 1
\][/tex]
- Range [tex]\(11-15\)[/tex]: Values in range: [tex]\(12, 15, 13, 12\)[/tex]
[tex]\[
\text{Number of Values: } 4
\][/tex]
- Range [tex]\(16-20\)[/tex]: Values in range: [tex]\(17, 17, 20, 18, 19\)[/tex]
[tex]\[
\text{Number of Values: } 5
\][/tex]
- Range [tex]\(21-25\)[/tex]: Values in range: [tex]\(25, 21\)[/tex]
[tex]\[
\text{Number of Values: } 2
\][/tex]
3. Calculate the total number of values:
[tex]\[
\text{Total number of values: } 15
\][/tex]
4. Calculate the relative frequency for each range:
The relative frequency is calculated by dividing the number of values in each range by the total number of values.
- Range [tex]\(1-5\)[/tex]:
[tex]\[
\text{Relative Frequency: } \frac{3}{15} = 0.2
\][/tex]
- Range [tex]\(6-10\)[/tex]:
[tex]\[
\text{Relative Frequency: } \frac{1}{15} \approx 0.0667
\][/tex]
- Range [tex]\(11-15\)[/tex]:
[tex]\[
\text{Relative Frequency: } \frac{4}{15} \approx 0.2667
\][/tex]
- Range [tex]\(16-20\)[/tex]:
[tex]\[
\text{Relative Frequency: } \frac{5}{15} \approx 0.3333
\][/tex]
- Range [tex]\(21-25\)[/tex]:
[tex]\[
\text{Relative Frequency: } \frac{2}{15} \approx 0.1333
\][/tex]
5. Complete the frequency table:
\begin{tabular}{|l|l|l|}
\hline Range & Number of Values & Relative Frequency \\
\hline [tex]$1-5$[/tex] & 3 & 0.2 \\
\hline [tex]$6-10$[/tex] & 1 & 0.0667 \\
\hline [tex]$11-15$[/tex] & 4 & \approx 0.2667 \\
\hline [tex]$16-20$[/tex] & 5 & \approx 0.3333 \\
\hline [tex]$21-25$[/tex] & 2 & \approx 0.1333 \\
\hline
\end{tabular}
Thus, the relative frequency for the range [tex]\(11-15\)[/tex] is approximately [tex]\(0.2667\)[/tex].
6. Answer Choices Comparison:
The closest match to our calculation of [tex]\(0.2667\)[/tex] is [tex]\(0.27\)[/tex].
Therefore, the relative frequency for the range [tex]\(11-15\)[/tex] is:
[tex]\[
\boxed{0.27}
\][/tex]
