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If there is no repeated numbers there is simply no mode. If there is two numbers that are the same, (example: 3,3) then that will be your mode. (Data: 3,3 Mode:3)
They could all be the same number, e.g. 55555 (mean=median=mode=5) or they could be three numbers the same, with an equal space between the first two and the last two, e.g. 24446 (mean=median=mode=4). For the mode to be well-defined, some of the numbers have to be the same.
The same as with any other quantity of numbers. To get the median of an even number of numbers, you average the middle two numbers.
If no two numbers are alike, then there is no mode. The mode is none.
The distribution is bi-modal. That is to say both the numbers are modes.