Find the median of the following data set:

[tex]\[ 0.32, 0.68, 1.05, 0.74, 0.60, 0.91 \][/tex]

A. 0.66

B. 0.71

C. 1.05



Answer :

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]