To find the median value of the data provided, follow these steps:
### Step 1: Combine All Data Elements into a Single List
First, we need to collect all elements from each row and combine them into a single list. This will be our flattened list.
Here are the elements from each row:
- Row 2: [tex]\(1, 2, 3, 5, 9\)[/tex]
- Row 3: [tex]\(4, 5, 5, 8\)[/tex]
- Row 4: [tex]\(0, 2, 5, 7\)[/tex]
- Row 5: [tex]\(1, 5\)[/tex]
- Row 6: [tex]\(1, 3, 8, 9\)[/tex]
Combining all these elements gives us:
[tex]\[ [1, 2, 3, 5, 9, 4, 5, 5, 8, 0, 2, 5, 7, 1, 5, 1, 3, 8, 9] \][/tex]
### Step 2: Sort the Combined Data List
Next, we need to sort the combined data list in ascending order:
[tex]\[ [0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 5, 5, 5, 7, 8, 8, 9, 9] \][/tex]
### Step 3: Calculate the Median
The median is the middle value of a sorted list.
If the number of elements [tex]\( n \)[/tex] in the list is odd, the median is the element at position [tex]\( \frac{n+1}{2} \)[/tex] (1-based index), or [tex]\( \frac{n-1}{2} \)[/tex] (0-based index).
If [tex]\( n \)[/tex] is even, the median is the average of the two middle elements.
In our sorted list, we have 19 elements:
[tex]\[ [0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 5, 5, 5, 7, 8, 8, 9, 9] \][/tex]
Since [tex]\( n = 19 \)[/tex], which is odd, the median will be the element at position [tex]\( \frac{19-1}{2} = 9 \)[/tex] (0-based index), which is the 10th element (1-based index).
### Step 4: Identify the Median Value
Counting to the 10th element in our sorted list, we find that the value is 5.
### Conclusion
The median value of the data is:
[tex]\[ 5 \][/tex]
