Let's find the median of the given data set: [tex]\(15, 18, 7, 11, 5\)[/tex].
### Step-by-Step Solution:
1. Arrange Data in Ascending Order:
First, we need to sort the data in ascending order:
[tex]\[
5, 7, 11, 15, 18
\][/tex]
2. Find the Number of Data Points:
Count the number of data points:
[tex]\[
n = 5
\][/tex]
3. Determine the Position of the Median:
Since the number of data points [tex]\( n \)[/tex] is odd, the median is located at the middle position. The middle position (when [tex]\( n \)[/tex] is odd) is given by:
[tex]\[
\text{Median position} = \left( \frac{n + 1}{2} \right) = \left( \frac{5 + 1}{2} \right) = 3
\][/tex]
4. Identify the Median Value:
Identify the value at the 3rd position in the sorted list:
[tex]\[
\text{Values in sorted order: } 5, 7, 11, 15, 18
\][/tex]
The value at the 3rd position is:
[tex]\[
11
\][/tex]
### Conclusion:
The median of the given data set [tex]\(15, 18, 7, 11, 5\)[/tex] is:
[tex]\[
\boxed{11}
\][/tex]
