Are you suggesting something like loading the first line of every table into an array, and performing a calculation upon that, then the next line, &c.? I might have a go at that.
Conrad's method seems to be working well enough for now. To determine accuracy I printed out a few select cells thus:

# @names is a list of file names, and I've created a matrix
# named after each file...
my $x = 3;
my $y = 3;
my @one;
print "one <- data.frame(a=c(";
foreach my $name (@names) {
  push (@one, @{$name}[$x]->[$y]);
}
print join(",", @one), "))\n";
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This provides a data frame one can stick into R and run mean(one) or sd(one), which for the examples I tested showed that conrad's results were accurate enough for my purposes. I must also compare punch_card_don's when I get an opportunity.