I agree with frozenwithjoy that you should use strict;. Always do that and also use warnings;

I did encounter an error when running your code, so I made just a few changes. One is replacing the C-style for loops with something a bit more Perlish. Also used List::Util to sum @scope_ct:

#!/usr/bin/perl -w
use strict;
use warnings;
use bignum;
use List::Util qw/sum/;

# pseudocode
#     print "Enter number of counts"
#     $ct = <>;
#    @arr = ();
#    for ($i = 0; $i < $ct; $i++) {
#        each iteration of loop calls subroutine
#        to get cell counts from user and stores in variable
#            push() variable to store in array
#         $count_i = &indiv_count()
#             push (@arr, $count_i);
#        }
#    output @arr
#        $arr_len = @arr;
#        print "The counts were:\n";
#        for ($j = 0; $j< $arr_len; $j++) {
#            print "Count number $j was arr[$j]\n";
#            }

my @arr;

print "Enter number of counts.\n->";

chomp( my $count = <> );
print "\n$count\n";

for ( 1 .. $count ) {
    print
"Enter individual count from scope.  Press Enter without input to end 
+list.\n";
    my $count_i = indiv_count();
    push @arr, $count_i;
}

print "The counts were:\n";
print "Count number $_ was $arr[$_-1]\n" for 1 .. @arr;

sub indiv_count {
    my @scope_ct;

    while ( chomp( my $input = <> ) ) {
        last if $input =~ /^\s*$/;
        push @scope_ct, $input;
    }

    my $scope_ct = @scope_ct;
    my $cell_sum = sum @scope_ct;

    my $cell_ct = ( $cell_sum / $scope_ct ) / 0.0000015;
    return $cell_ct;
}
[download]

Didn't encounter any more errors, but I may not have sufficiently tested it.

Hope this helps!

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