To determine the median of a set of data, the steps involve organizing the data in increasing order and then finding the middle value. If the number of data points is odd, the median is the middle number. If the number of data points is even, the median is the average of the two middle numbers.
Here is the step-by-step solution for obtaining the median of the given data:
1. List the Data: The given set of numbers is:
```
2, 2, 2, 2, 3, 2, 3, 3, 5, 5, 21, 45, 94, 45, 56, 49, 41, 36, 31, 26, 19, 12, 5, 2, 2, 2, 2, 2, 2, 2, 7, 7, 53, 515, 12, 41, 24, 26, 31, 36, 46, 41, 441, 45, 48, 4, 56
```
2. Sort the Data: Arrange these numbers in ascending order:
```
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 12, 12, 19, 21, 24, 26, 26, 31, 31, 36, 36, 41, 41, 41, 45, 45, 45, 46, 48, 49, 53, 56, 56, 94, 441, 515
```
3. Determine the Number of Data Points:
- The total number of data points [tex]\( n \)[/tex] is 43 (this was counted from the sorted list).
4. Find the Median:
- Since [tex]\( n \)[/tex] is odd (43), the median is the value at the position [tex]\( (n+1)/2 \)[/tex].
- Calculating the position: [tex]\( (43+1)/2 = 22 \)[/tex].
- The 22nd value in the sorted list is the 22nd element.
5. Identify the 22nd Element in the Sorted List:
- When counting the sorted list to the 22nd position, we find:
```
2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 3, 3, 3, 5, 5, 12, 12, 19,
21, 24, 26, 26, 31, 31, 36, 36, 41, 41,
41, 45, 45, 45, 46, 48, 49, 53, 56, 56,
94, 441, 515
```
- The 22nd element is 19.
Therefore, the median of the dataset is 19.
