If you can everything together, and then divide by the number of items in the dataset, there must be a mean. However whether that figure will actually in anyway be meaningful depends upon the distribution of the data.
If all of the data items are distinct, with none of them being repeated, there won't be a meaningful mode.
If the data items can be ordered, there must be a median (but, once again, whether it's actually of any real value when describing the dataset will depend upon the structure of the distribution).