When is the mean the median and the mode the same?

Answer 1

It's a bit difficult to answer the question as asked, though it's fairly easy to give specific cases where it is true.

One (although not the only) example would be when the data consist of a single value. If your dataset is (2, 2, 2, 2, 2) then the median, the mode, and the mean are all 2.

Another example that's a bit less trivial is (1, 2, 2, 2, 3) where again the median, the mode, and the mean are all 2.