To find the median of the given set of numbers, [tex]$1.1, 1.3, 1.5, 1.2, 1.9, 0.7$[/tex], and [tex]$1.1$[/tex], follow these steps:
1. List the numbers in ascending order: Organize the numbers from the smallest to the largest.
Given numbers: [tex]$1.1, 1.3, 1.5, 1.2, 1.9, 0.7, 1.1$[/tex]
Sorted numbers: [tex]$0.7, 1.1, 1.1, 1.2, 1.3, 1.5, 1.9$[/tex]
2. Count the total number of observations: In this case, there are 7 numbers in the list.
3. Determine the position of the median:
Since the total number of observations (7) is odd, the median will be the middle number. The position of the median can be found using the formula:
[tex]\[
\text{Median position} = \frac{n + 1}{2}
\][/tex]
where \( n \) is the total number of observations.
Substituting \( n = 7 \):
[tex]\[
\text{Median position} = \frac{7 + 1}{2} = 4
\][/tex]
4. Identify the median:
The 4th number in the sorted list [tex]$0.7, 1.1, 1.1, 1.2, 1.3, 1.5, 1.9$[/tex] is [tex]$1.2$[/tex].
Thus, the median of the numbers [tex]$1.1, 1.3, 1.5, 1.2, 1.9, 0.7,$[/tex] and [tex]$1.1$[/tex] is [tex]$\boxed{1.2}$[/tex].
