After downloading the file you gave in your post, I was able to write a program that parsed it and produced the averages.

There is no error checking, so the file must be in the order you described. 

#!/usr/bin/perl
use strict;
use warnings;
use List::Util 'sum';
# pm 1158142

open my $fh, '<', 'j2.txt' or die $!;
my (undef, @percent) = split /[\s%]+/, <$fh>; #split on spaces and % s
+ign
my ($gene, @data) = split ' ', <$fh>;
close $fh or die $!;

my $limit = 10;
my $start = 0;
my @avgs;

print join("\t", $gene, map {sprintf "Average_%d%%", 10 * $_} 1 .. 10)
+, "\n"; 

for my $i (0 .. $#percent) {
    if ($percent[$i] <= $limit) {
        if ($percent[$i] == $limit) {
            push @avgs, sprintf "%.16f",
                sum(@data[$start..$i]) / ($i+1 - $start);
                
            if ($limit == 100) {
                print join("\t", @avgs), "\n";
                @avgs = ();
        
                $limit = 10;
                $start = $i+1;    
            }
            else {
                $limit += 10;
                $start = $i+1;    
            }
        }
    }
    else {
        push @avgs, sprintf "%.16f",
            sum(@data[$start..$i-1]) / ($i - $start);
            
        $limit += 10;
        $start = $i;
    }
}

[download]
It produced the following output. 
Gene1    Average_10%    Average_20%    Average_30%    Average_40%    A
+verage_50%    Average_60%    Average_70%    Average_80%    Average_90
+%    Average_100%
0.0085539803980398    0.0029112286228623    0.0125793829382938    0.01
+16449144914491    0.0184377812781278    0.0050317531753175    0.01067
+45049504950    0.0020127012701270    0.0106745049504950    0.02959749
+09990999
0.0136619722578318    0.0178790606333361    0.0063430585482791    0.01
+45855494640373    0.0112920382947386    0.0053672033870054    0.01976
+10670157925    0.0146378274191056    0.0108215366991245    0.02352507
+97807054
0.0164707828807572    0.0136918453750137    0.0079514124251931    0.01
+20488239300120    0.0010953476300011    0.0159028248503863    0.00821
+51072250082    0.0079514124251931    0.0071197595950071    0.01752556
+20800175
0.0201577409649362    0.0194378216447599    0.0078664354985117    0.00
+71113981627170    0.0184896352230643    0.0167161754343373    0.02133
+41944881511    0.0172078276529943    0.0066373049518692    0.03887564
+32895198
0.0104368645819806    0.0270142152808031    0.0038451606354665    0.01
+00641194183384    0.0158907148710607    0.0109861732441901    0.01059
+38099140405    0.0197751118395422    0.0143016433839546    0.02330638
+18108890
0.0068663582776188    0.0225118460673360    0.0068663582776188    0.01
+50078973782240    0.0101524011676221    0.0146482309922535    0.01633
+21236174791    0.0151059882107614    0.0163321236174790    0.04193383
+09097434
0.0157328709970234    0.0251269401749335    0.0044248699679128    0.01
+46968895362819    0.0151709827471297    0.0176994798716513    0.01469
+68895362819    0.0162245232156804    0.0194378216447599    0.03223833
+83376506
0.0095465981450263    0.0179928578674928    0.0052072353518326    0.00
+62765783258696    0.0234325590832465    0.0099805344243457    0.01046
+09638764493    0.0156217060554976    0.0133900337618551    0.01129784
+09865652
0.0101156314461855    0.0097543588945361    0.0036127255164948    0.00
+27869596841532    0.0104510988155744    0.0180636275824742    0.04250
+11351833357    0.0245665335121649    0.0195087177890721    0.02229567
+74732253
0.0117016829888117    0.0178659624204179    0.0053632713698720    0.00
+75225104928075    0.0042314121522042    0.0234033659776234    0.01457
+48640798146    0.0082886921170750    0.0155151778914155    0.03432145
+41234343
0.0051755175517552    0.0188536710813939    0.0074757475747575    0.01
+88536710813938    0.0088723158030089    0.0235773577357736    0.01219
+94342291372    0.0241524152415241    0.0199627105567700    0.03881638
+16381638
0.0256052955722923    0.0146810285424147    0.0083044201856083    0.01
+20117506256120    0.0120117506256120    0.0083044201856083    0.02202
+15428136220    0.0145327353248145    0.0073405142712073    0.02402350
+12512240
0.0163571912746830    0.0146463625954432    0.0144099065991255    0.01
+42708148365857    0.0105153372480105    0.0272619854578050    0.02516
+16998434537    0.0319354686791430    0.0255372476023112    0.02516169
+98434537

[download]
Hope this helps.

List::Util was added to perl core in version 5.08.

In reply to Re: Average columns based on header name by Cristoforo
in thread Average columns based on header name by jacobs.smith

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