I never did it, but from similar experiences with variables I would:

Create a variable text called... I. don't know.. avg_or_median...

Set up a dropdown manual, 2 options. Each option sets the variable ave_or_median to either AVG or MEDIAN (or whatever is called the operation)

In your KPI's and PQL, use the variable ... like <%=avg_or_median%>(table.column)

Probably you will need some try and error.

Using KPI with parameters is another way to try, but I am not completely confident it will work

HTH

Thanks for the insights, however I was not able to find these options you mention (which I also know from Analyses) in the View.

My bad, I didn't realise that you were in views.

with Views you can use several buttons (one per option, in your case 2 buttons one with Avg and another with Median)  

Also a Input checkbox, then switching between the 2 values (but you need to edit yaml)

Hope it helps!