To find the median of the numbers [tex]$11, 10, 12, 9, 14, 10, 8, 16, 4, 12$[/tex], we follow these steps:
1. List the Numbers: First, list all the given numbers.
[tex]$11, 10, 12, 9, 14, 10, 8, 16, 4, 12$[/tex]
2. Sort the Numbers: Arrange the numbers in ascending order.
[tex]$4, 8, 9, 10, 10, 11, 12, 12, 14, 16$[/tex]
3. Determine the Number of Elements: Count the number of elements in the list.
Here, we have [tex]$10$[/tex] elements.
4. Identify the Middle Position:
- For an even number of elements, the median is the average of the two middle numbers.
- The two middle positions in an even list are [tex]$\frac{n}{2}$[/tex] and [tex]$\frac{n}{2} + 1$[/tex] where [tex]$n$[/tex] is the total number of data points.
In our case, [tex]$n=10$[/tex], so the middle positions are [tex]$5$[/tex] and [tex]$6$[/tex] (since [tex]$\frac{10}{2}=5$[/tex] and [tex]$\frac{10}{2}+1=6$[/tex]).
5. Find the Numbers Corresponding to These Positions: Locate the fifth and sixth numbers in the sorted list.
The fifth number is [tex]$10$[/tex], and the sixth number is [tex]$11$[/tex].
6. Calculate the Median: The median is the average of these two middle numbers.
[tex]\[
\text{Median} = \frac{10 + 11}{2} = \frac{21}{2} = 10.5
\][/tex]
So, the median of the numbers [tex]$11, 10, 12, 9, 14, 10, 8, 16, 4, 12$[/tex] is [tex]$10.5$[/tex].
Additionally, the sorted list of numbers is [tex]$[4, 8, 9, 10, 10, 11, 12, 12, 14, 16]$[/tex] and the middle index positions used were [tex]$5$[/tex] and [tex]$6$[/tex].
