What I am having trouble understanding is how to make an array with an uknown length?

It's common to have to work with an array without knowing its length--in Perl or other computer languages. Consider the following:

use strict;
use warnings;

my @array = qw/5 8 2 78 5 1 9 9 16/;

# Example 1
for my $number (@array) {
    print $number, "\n";
}

# Example 2
print "\n", 'Number of elements in @array: ', scalar @array;

# Example 3
print "\n\n", 'Number of elements in @array: ', $#array + 1, "\n\n";

# Example 4
for ( my $i = 0 ; $i < @array ; $i++ ) {
    print $array[$i], "\n";
}

# Example 5
my $total;
for my $number (@array) {
    $total += $number;
}

print "\n", '$total is: ', $total;
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First, notice the following at the top of the script:

use strict;
use warnings;
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Always have these, as they'll preemptively catch issues in your scripts, potentially saving your hours of headaches. (Omit them, however, if you prefer these headaches... :)

All the Examples could be working with an array of an unknown length. It just so happens that we know the length, since we've initialized it.

Example 1 iterates through each element of @array, assigning $number an each element's value that's then printed within the loop. Examples 2 & 3 show the number of elements in @array:

Number of elements in @array: 9
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Example 4 shows a more traditional C-style for loop, and produces the same output as Example 1:

5
8
2
78
5
1
9
9
16
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Example 5 shows one way to get the sum of the numbers in @array, and here's its output:

$total is: 133
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Perhaps the above will assist you with how to "Find the average of the numbers in an array (@nums) of unknown length."

Hope this helps!