Do professors from different fields use the same data set in different ways? I have no experience with data analysis but a data analysis project was offered to me in the past by one of my math professors.  It would have been a PCA project, where PCA means "Principle Component Analysis" -- equivalent to the "singular value decomposition" in linear algebra.

It was a biology data set.

My question is:  would a biologist professor use this data set in some different way?  If yes, then in what ways other than something linear algebraic?

What would / could a statistics professor do with this biology data set that would be different from what a mathematician and biologist does with it?

Thanks,
Yes.  The number of ways to analyze data is very large.  If the data is complex, it would be unlikely any two people would pick the same approach.  Keep in mind that analysis methods are selected from the knowledge of the user to suit the goals of the user.  Analysis methods are only partially selected based on the actual content of the data set.