# Mode for unique numbers

I'm trying to construct a rough statistical software and I'm confused about the following:

1. What is the mode if all numbers are unique?
2. What is the mode if 2 numbers have same (highest) frequency?

What I feel:

1. Should output nothing.
2. Should output the average of the 2.

Just as reference:

a = [1 2 3 4 5]
mode(a) %Prints 1
a = [2 2 3 3]
mode(a) %Prints 2


in Octave

But I'm not sure how it's supposed to be done.

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For 2.: then you have two modes (i.e. your data is bimodal). –  Guess who it is. Jul 7 '12 at 10:00
@J.M., in that case, if all elements are unique, I should have $n$ modes? –  Inquest Jul 7 '12 at 10:01

In general, a data set can have multiple modes. If you must return a single value, pick any one of them. (Octave seems to pick the least one.) But don't pick something that isn't a mode. So don't use your second idea: when asked for the mode of $[1,1,2,5,5]$, the value $3$ is not a sensible answer.
So, I assume there isn't some International standard about what to choose as mode? I think I'd rather output all possibilities and put out a warning to the user about what I'm doing. If there are $n$ modes, isn't it a good idea to use the median of these $n$ modes as the true mode? –  Inquest Jul 7 '12 at 10:10