To find the median of a dataset, we must first rearrange the data in either ascending or descending order.
Original dataset: 1, 1, 1, 2, 4, 5, 6, 7
New dataset with Michael's 4 pairs of shoes added: 1, 1, 1, 2, 4, 4, 5, 6, 7
For datasets with an odd number of values, the median is simply the middle value when the data is sorted. For datasets with an even number of values, the median is the average of the two middle values when the data is sorted.
Original dataset median: (2 + 4) / 2 = 3
New dataset median: 4
Therefore, the median of the original dataset is 3 and the median of the new dataset after Michael's 4 pairs of shoes is added is 4.