I've made progress but I'm still having trouble getting the image to display in the browser, I'm hoping I can get input from someone.

The following code prints the A OK message and then prints

Content-type: image/png Content-type: text/html 
Software error:
Failed to open pipe: No such file or directory

#!/usr/bin/perl -w

use CGI qw( :standard );
use CGI::Carp 'fatalsToBrowser';   

print "Content-type: text/plain\n\n";
print p( "A OK" );
print "Content-type: image/png\n\n";

my $data = "05056670.txt";

my $plot = plotdata();

sub plotdata {
  open my $graph => "| gnuplot" or die "Failed to open pipe: $!\n";
  my $graph;
  print $graph <<"gnu";
  set terminal png color
  set output
  set xdata time
  set timefmt "%Y%m%d"
  set key left top title "Legend" box
  set grid xtics ytics
  set yrange [700:]
  set format x "%Y"
  set xlabel "Year"
  set ylabel "Sodim, water, filtered, milligrams per liter"
  set title "05056670 Western Stump Lake Major Ions"
  plot "$data" using 2:3 title "P00930 Sodium dissolved"
gnu
  close $graph or die "Failed to close pipe: $!\n";
}
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The following code appears to work at the command prompt because it prints the text and a bunch of strange characters, but it this is what the browser shows:

A OK 

Content-Type: image/png 

no image.

!/usr/bin/perl -w
use CGI qw( :standard );
use CGI::Carp 'fatalsToBrowser';  
my $q = new CGI;
print $q->header("text/html");
print p(" A OK ");
my $img = `gnuplot setcmds`;
print $q->header("image/png"), $img;
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setcmds file:

set terminal png color
set output
set xdata time
set timefmt "%Y%m%d"
set key left top title "Legend" box
set grid xtics ytics
set yrange [700:]
set format x "%Y"
set xlabel "Year"
set ylabel "Sodim, water, filtered, milligrams per liter"
set title "05056670 Western Stump Lake Major Ions"
plot "05056670.txt" using 2:3 title "P00930 Sodium dissolved"
[download]

I'm sure I'm not doing something correctly, but I don't know what.