To find the median of the given data set, we will follow these steps:
1. List the Data:
The given data points are: 7, 16, 12, 7, 19, 5, 12, 18.
2. Sort the Data:
First, we need to sort the data in ascending order: 5, 7, 7, 12, 12, 16, 18, 19.
3. Find the Number of Data Points:
Count the number of elements in the sorted list. There are 8 data points in total.
4. Determine if the Number of Data Points is Odd or Even:
Since the number of data points (8) is even, the median will be the average of the two middle numbers.
5. Identify the Middle Numbers:
The two middle numbers in the sorted list are the 4th and 5th elements: 12 and 12.
6. Calculate the Median:
Since the number of elements is even, find the average of the two middle numbers:
[tex]\[
\text{Median} = \frac{12 + 12}{2} = 12.0
\][/tex]
7. Round the Median if Necessary:
In this case, the median is already a whole number, so no rounding is needed. For completeness, we note that it would be rounded to two decimal places: 12.00.
Therefore, the median of the given data set is [tex]\( \boxed{12.00} \)[/tex].
