... when I add use strict; it gives me errors ...

I don't know the current state of your code and so cannot say why it will not compile with use strict; What do the error messages say?

How would I go about making my variables constant rather than mutable global ...

Variables (that actually vary) are good. The point is to use variables that have as narrow a scope as (reasonably) possible. This practice will save you a lot of programming grief. Declaring variables at the top of your program and then accessing them deep within a function is your ticket for a roller-coaster ride to Hell.

Another parenthetic thought: the statements
    print above_mean(@list_of_numbers);
or
    print above_mean();
from the code above print the value returned by a call to above_mean(), but what does this function actually return? Is it anything useful? (IOW: The function already prints a bunch of stuff during its execution, what's the point of printing its return value, whatever it may be?)