Final answer:
Adding a shoe size of 9.5 to the original data does not change the median; it remains at 6.5, as the new size is added to the end of the ordered list.
Step-by-step explanation:
When analyzing the median of a set of data, it is important to first arrange the data in numerical order. Adding a new data point can affect the median, especially if the number of data points is even. With the current shoe sizes listed (5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5), we have 10 shoes - an even number. The median would be the average of the 5th and 6th sizes when sorted. In this case, the median is between 6.5 and 6.5, so the median is 6.5.
Adding a shoe size of 9.5 to the data changes the total count to 11, which is an odd number, so the median becomes the middle value, which is the 6th shoe size when sorted. With the new size added, the ordered list becomes (5, 5.5, 6, 6.5, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9.5). Now, the median becomes 6.5 without any change even after adding the new size of 9.5 because it falls to the right of the original median value.