Sure, let's address the problem step by step for the given data set [tex]\( 3, 4, 4, 5, 8, 8, 9, 10, 11 \)[/tex].
### Step-by-Step Solution:
1. List the Data Set:
The given data set is [tex]\( 3, 4, 4, 5, 8, 8, 9, 10, 11 \)[/tex].
2. Determine the Median:
Since the data set is already arranged in ascending order and it contains 9 elements (an odd number), the median is the middle value.
Breaking the data set into individual elements:
[tex]\[
3, 4, 4, 5, 8, 8, 9, 10, 11
\][/tex]
The middle value (5th element) is 8.
Hence, the median of the data set is 8.
3. Split the Data Set:
We then split the data into two parts:
- The left part consists of all elements before the median.
- The right part consists of all elements after the median.
When we divide [tex]\( 3, 4, 4, 5, 8, 8, 9, 10, 11 \)[/tex] as per the median:
- Left part: [tex]\( 3, 4, 4, 5 \)[/tex]
- Median: [tex]\( 8 \)[/tex]
- Right part: [tex]\( 8, 9, 10, 11 \)[/tex]
### Result:
Therefore, the final result of the problem can be expressed as:
[tex]\[
\left( [3, 4, 4, 5], 8, [8, 9, 10, 11] \right)
\][/tex]
This correctly represents the data set split into the left part, median, and right part.
