To find the median of the given data set, follow these steps:
1. Arrange the Data in Ascending Order:
First, we need to sort the data in ascending order. The given data set is:
[tex]\[
0.32, 0.68, 1.05, 0.74, 0.6, 0.91, 0.66, 0.71, 1.05
\][/tex]
Arranging these numbers in ascending order gives us:
[tex]\[
0.32, 0.6, 0.66, 0.68, 0.71, 0.74, 0.91, 1.05, 1.05
\][/tex]
2. Determine the Number of Data Points:
Count the number of data points in the sorted list. There are 9 data points.
3. Identify the Median:
The median is the middle value of a data set. Since the number of data points is odd (9), the median is the value at the (n + 1) / 2 position, where n is the number of data points.
[tex]\[
(9 + 1) / 2 = 10 / 2 = 5
\][/tex]
So, the median is the 5th value in the sorted list.
4. Locate the Median in the Sorted List:
Looking at the sorted list:
[tex]\[
0.32, 0.6, 0.66, 0.68, 0.71, 0.74, 0.91, 1.05, 1.05
\][/tex]
The 5th value is 0.71.
So, the median of the given data set is [tex]\( 0.71 \)[/tex].
Additionally, the position of the median (midpoint) in the sorted list is 4 (considering 0-based indexing, where the first element is at position 0).
Thus, the final answer is:
[tex]\[
\left(4, 0.71\right)
\][/tex]
