To solve this question, follow these steps:
### Step 1: Organize the Data Set
First, let's list the data set in ascending order. The provided data set is [tex]\[3, 7, 8, 6, 6, 5, 1, 4\][/tex].
Sorting these values in ascending order gives us:
[tex]\[1, 3, 4, 5, 6, 6, 7, 8\][/tex]
### Step 2: Find the Median
The median is the middle value of a data set when it is arranged in ascending order. If the number of data points (n) is odd, the median is the middle number. If n is even, the median is the average of the two middle numbers.
In our sorted data set, we have 8 numbers:
[tex]\[1, 3, 4, 5, 6, 6, 7, 8\][/tex]
Since 8 is an even number, we have two middle values: the 4th and 5th elements.
The 4th value is 5, and the 5th value is 6.
The median is the average of these two middle numbers:
[tex]\[
\text{Median} = \frac{5 + 6}{2} = \frac{11}{2} = 5.5
\][/tex]
### Step 3: Verify the Given Mean
We are given that the mean (average) of the data set is 5. This helps to verify that the data values are correct.
### Summary
- Organized Data Set: [tex]\([1, 3, 4, 5, 6, 6, 7, 8]\)[/tex]
- Mean: [tex]\(5\)[/tex] (as provided)
- Median: [tex]\(5.5\)[/tex]
Thus, the median of the given data set is [tex]\(5.5\)[/tex].
