You can fit a curve of the form "Ax^2 + Bx + C = y" to the data. The package Statistics::Regression can be used to do it. (Make sure you edit Regression.pm to turn off DEBUGGING first): 
use strict;
use Statistics::Regression;

my $reg= Statistics::Regression->new( 3, "quad regression", [ "const",
+ "X", "X^2" ] );
              
my @array = ('62.6',    '62.8',    '63',    '63.3',    '63.5',    '63.
+7',    '64');
my @array2 = ('7.476',    '7.5219', '7.5464', '7.5516', '7.5504',    '
+7.5372', '7.518');
my $i;
for $i (0..$#array) {
   my $x = $array[$i];
   my $x2 = $x * $x;
   my $y = $array2[$i];
   $reg->include($y, [1.0, $x, $x2]);
}
              
my $theta = $reg->theta();
print "Coefficients: ",join(",",@$theta),"\n";
my $c = $theta->[0];
my $b = $theta->[1];
my $a = $theta->[2];

print "\nComputed results:\n";
for $i (0..$#array) {
   my $x = $array[$i];
   my $y = ($a*$x + $b)*$x + $c;
   my $ytrue = $array2[$i];
   print "$x\t$y\t($ytrue)\n";
}

# Solve for the derivative being 0.
my $maxx = -$b/(2.0*$a);
my $maxy = ($a*$maxx + $b)*$maxx + $c;
print "\nPeak point:\n";
print "$maxx\t$maxy\n";

[download]
Don't count on a very accurate fit with so few data points. Once you have a quadratic equation, solve for the peak using "2Ax + B = 0". Again, don't count on great accuracy with this method.

Here is what I got: 

Coefficients: -451.490758046837,14.4832720403469,-0.11423976795752

Computed results:
62.6    7.48383859766494        (7.476)
62.8    7.51535962535968        (7.5219)
63      7.53774147161789        (7.5464)
63.3    7.55417827581152        (7.5516)
63.5    7.55371216847811        (7.5504)
63.7    7.54410687970818        (7.5372)
64      7.51256298135968        (7.518)

Peak point:
63.3897998012935        7.5550995057929

[download]

In reply to Re: mathsy question by tall_man
in thread mathsy question: finding max of curve from discrete points by Anonymous Monk

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