It sounds like you're crying out for modules (or better, object classes ;)

If you need to be calling only certain subroutines from the command line, this is the ideal (imo) way to go.
Instead of avg_routines.pl, make it AvgRoutines.pm. This will also require changing parts of it (adding a 'package' line to the top, at least) to turn it into its own package.

Here's a simple example:

package AvgRoutines;
sub avg3 {
    # ... code ...
}
1;
[download]

See Simple Module Tutorial for a simple introduction to modules, if you need it. For a more technical primer, see perlmod.

Now, with it being its own module you can call just the sub you need from the command line *or* from other scripts (by use'ing it).

cat some_file_holding3numbers.txt | perl -I'.' -MAvgRoutines -pe 'AvgRoutines::avg3($_)' > avg.txt
See perlrun for any help with those command line switches.