Mode of a PDF - all data are unique

[abhipatel]

Question is what is the mode when all data are unique? have a set wherein the actual question is what is the inference about the PDF for the data? Median > mean but no mode...i was under the impression that PDF is only for a continuous measurements...when data set is unique...in which case it should be a probability function & not PDF.

Please confirm...what is the mode and what if anything would the PDF look like in this case

 

[statdad]

The typical definition is that if all data values are different the data set does not have a mode.
I'm not sure what the rest of your question means - what kind of inference?
The abbreviation PDF is used for both of the following:

1. Probability density function (most common)
2. Probability distribution function (less common, but still done)

To which are you referring?

 

[HallsofIvy]

If you have a distribution with a finite number of outcomes, each assigned a probabilty (which, of course, sums to 1), then that function (which, I think, is what you are calling the "probability function") is or at least corresponds to the PDF. It might be clearer if you were to show the entire problem.