To find the difference between the median of the data including the outlier and excluding the outlier, we need to follow these steps:
1. Identify and sort the data:
The given data is: 55, 52, 56, 48, 57, 20, 45, 41
When sorted in ascending order: 20, 41, 45, 48, 52, 55, 56, 57
2. Calculate the median including the outlier:
Since there are 8 numbers, the median will be the average of the 4th and the 5th values in the sorted list.
- The 4th value (48) and the 5th value (52)
- Median including outlier = (48 + 52) / 2 = 50.0
3. Identify the outlier:
Here, the outlier is the value 20, which is noticeably different from the other values.
4. Remove the outlier and sort the remaining data:
The remaining data is: 55, 52, 56, 48, 57, 45, 41
Sorted in ascending order: 41, 45, 48, 52, 55, 56, 57
5. Calculate the median excluding the outlier:
Since there are now 7 numbers, the median will be the middle value (4th value in the sorted list).
- Median excluding outlier = 52
6. Calculate the difference between the two medians:
- Difference = Median including outlier - Median excluding outlier
- Difference = 50.0 - 52 = -2.0
Thus, the difference between the median of the data including the outlier and excluding the outlier is -2.0, and the correct choice is 2.
