Since you're checking $divide_by for a true value (Truth and Falsehood), it's likely that $data_to_sum[0]->[$c] is empty, as LanX pointed out (Update before posting: and as you just discovered yourself). I just wanted to point out tip #4 from the Basic debugging checklist: Use Data::Dumper to see what the variables really contain (although personally I prefer Data::Dump):

use Data::Dump;
dd $data_to_sum[0]->[$c], $divide_by;
$data_to_sum[0]->[$c] /= $divide_by if $divide_by;
print $data_to_sum[0]->[$c], "\n";
__END__
("", 123)
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Update: Actually, it turns out that using Data::Dump in this case might confuse the issue more, since it has an issue that causes it to silence the warning in question. So in this case, I recommend Data::Dumper, and I would recommend turning on its Useqq option (as it makes issues with control characters in the string easier to spot):

use Data::Dumper;
$Data::Dumper::Useqq=1;
print Dumper($data_to_sum[0]->[$c], $divide_by);
$data_to_sum[0]->[$c] /= $divide_by if $divide_by;
print $data_to_sum[0]->[$c], "\n";
__END__
$VAR1 = "";
$VAR2 = 123;
Argument "" isn't numeric in division (/) at ...
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Update 2019-08-17: Updated the link to "Truth and Falsehood".