If one 5 is added to it {1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4, 5} , will this make the result different?
thanks.
To 50418129, thanks for your reply. Your suggestion refers to either a multi-mode or a no-mode option. But these two options are contradictory to each other.
To: 那些年, thanks for your comment. I tried to figure out the rules from your work. If all distinct sample elements have the same frequency, then there will be no mode; otherwise the mode(s) will be the one(s) with the highest frequency. The result can be a single mode or multi-modes.
This is convincing. In this case, the sample {1,1,1,1,1} will have no mode ! Is that correct? I was wondering if this is your guess or there is an official definition of mode somewhere in the net. I would be grateful if you could point me to the relevant site(s). Many thanks.
To Ping Fai, thanks for your reply. I quote the following from wiki, ” The mode is not necessarily unique, since the prob density function may take the same maximum value at several points x1, x2, etc. The most extreme case occurs in uniform distributions, where all values occur equally frequently.
It seems that your view got a support from Wiki. I recall many previous Q&A solutions in this forum assumed no mode for a simple uniform distribution. E.g. {1,2,3,4} has no mode but there are 4 modes from your definition.
In your view, the only no mode scenario happens in an empty sample space { }. This can be debatable. Many thanks for your reply. Let’s see if there are other replies to this question.