# The LearningOnline Network with CAPA
#
# $Id: lonproblemstatistics.pm,v 1.47 2003/03/27 19:26:33 matthew Exp $
#
# Copyright Michigan State University Board of Trustees
#
# This file is part of the LearningOnline Network with CAPA (LON-CAPA).
#
# LON-CAPA is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# LON-CAPA is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with LON-CAPA; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
#
# /home/httpd/html/adm/gpl.txt
#
# http://www.lon-capa.org/
#
# (Navigate problems for statistical reports
#
###############################################
###############################################

=pod

=head1 NAME

lonproblemstatistics

=head1 SYNOPSIS

Routines to present problem statistics to instructors via tables,
Excel files, and plots.

=over 4

=cut

###############################################
###############################################

package Apache::lonproblemstatistics;

use strict;
use Apache::lonnet();
use Apache::lonhtmlcommon;
use Apache::loncoursedata;
use Apache::lonstatistics;
use Spreadsheet::WriteExcel;

###############################################
###############################################

=pod 

=item &CreateInterface()

Create the main intereface for the statistics page.  Allows the user to
select sections, maps, and output.

=cut

###############################################
###############################################
sub CreateInterface {
    my $Str = '';
    $Str .= '<table cellspacing="5">'."\n";
    $Str .= '<tr>';
    $Str .= '<td align="center"><b>Sections</b></td>';
    $Str .= '<td align="center"><b>Sequences and Folders</b></td>';
    $Str .= '<td align="center"><b>Output</b></td>';
    $Str .= '</tr>'."\n";
    #
    $Str .= '<tr><td align="center">'."\n";
    $Str .= &Apache::lonstatistics::SectionSelect('Section','multiple',5);
    $Str .= '</td><td align="center">';
    #
    my $only_seq_with_assessments = sub { 
        my $s=shift;
        if ($s->{'num_assess'} < 1) { 
            return 0;
        } else { 
            return 1;
        }
    };
    $Str .= &Apache::lonstatistics::MapSelect('Maps','multiple,all',5,
                                              $only_seq_with_assessments);
    $Str .= '</td><td>'."\n";
    $Str .= &CreateAndParseOutputSelector();
    $Str .= '</td></tr>'."\n";
    $Str .= '</table>'."\n";
    return $Str;
}

#######################################################
#######################################################

=pod

=item &CreateAndParseOutputSelector()

Construct a selection list of options for output and parse output selections.
The current output selected is indicated by the values of the two package
variables $output_mode and $show.  @OutputOptions holds the descriptions of
the output options and the values for $output_mode and $show.

 Based on code from lonstudentassessment.pm.

=cut

#######################################################
#######################################################
my $output_mode;
my $show;

my @OutputOptions = 
    (
     { name  => 'problem statistics grouped by sequence',
       value => 'HTML problem statistics grouped',
       description => 'Output statistics for the problem parts.',
       mode => 'html',
       show => 'grouped',
     },
     { name  => 'problem statistics ungrouped',
       value => 'HTML problem statistics ungrouped',
       description => 'Output statistics for the problem parts.',
       mode => 'html',
       show => 'ungrouped',
     },
     { name  => 'problem statistics, Excel',
       value => 'Excel problem statistics',
       description => 'Output statistics for the problem parts '.
           'in an Excel workbook',
       mode => 'excel',
       show => 'all',
     },
     { name  => 'Degree of Difficulty Plot',
       value => 'plot deg diff',
       description => 'Generate a plot of the degree of difficulty of each '.
           'problem part.',
       mode => 'plot',
       show => 'deg of diff',
     },
     { name  => 'Percent Wrong Plot',
       value => 'plot per wrong',
       description => 'Generate a plot showing the percent of students who '.
           'were unable to complete each problem part',
       mode => 'plot',
       show => 'per wrong',
     },
     );

sub OutputDescriptions {
    my $Str = '';
    $Str .= "<h2>Output Modes</h2>\n";
    $Str .= "<dl>\n";
    foreach my $outputmode (@OutputOptions) {
	$Str .="    <dt>".$outputmode->{'name'}."</dt>\n";
	$Str .="        <dd>".$outputmode->{'description'}."</dd>\n";
    }
    $Str .= "</dl>\n";
    return $Str;
}

sub CreateAndParseOutputSelector {
    my $Str = '';
    my $elementname = 'statsoutputmode';
    #
    # Format for output options is 'mode, restrictions';
    my $selected = 'HTML problem statistics grouped';
    if (exists($ENV{'form.'.$elementname})) {
        if (ref($ENV{'form.'.$elementname} eq 'ARRAY')) {
            $selected = $ENV{'form.'.$elementname}->[0];
        } else {
            $selected = $ENV{'form.'.$elementname};
        }
    }
    #
    # Set package variables describing output mode
    $output_mode = 'html';
    $show        = 'all';
    foreach my $option (@OutputOptions) {
        next if ($option->{'value'} ne $selected);
        $output_mode = $option->{'mode'};
        $show        = $option->{'show'};
    }
    #
    # Build the form element
    $Str = qq/<select size="5" name="$elementname">/;
    foreach my $option (@OutputOptions) {
        $Str .= "\n".'    <option value="'.$option->{'value'}.'"';
        $Str .= " selected " if ($option->{'value'} eq $selected);
        $Str .= ">".$option->{'name'}."<\/option>";
    }
    $Str .= "\n</select>";
    return $Str;
}

###############################################
###############################################

=pod 

=item &Gather_Student_Data()

Ensures all student data is up to date.

=cut

###############################################
###############################################
sub Gather_Student_Data {
    my ($r) = @_;
    my $c = $r->connection();
    #
    my @Sequences = &Apache::lonstatistics::Sequences_with_Assess();
    #
    my @Students = @Apache::lonstatistics::Students;
    #
    # Open the progress window
    my %prog_state=&Apache::lonhtmlcommon::Create_PrgWin
        ($r,'Statistics Compilation Status',
         'Statistics Compilation Progress', scalar(@Students));
    #
    while (my $student = shift @Students) {
        return if ($c->aborted());
        my ($status,undef) = &Apache::loncoursedata::ensure_current_data
            ($student->{'username'},$student->{'domain'},
             $ENV{'request.course.id'});
        &Apache::lonhtmlcommon::Increment_PrgWin($r,\%prog_state,
                                                 'last student');
    }
    &Apache::lonhtmlcommon::Close_PrgWin($r,\%prog_state);
    $r->rflush();
}

###############################################
###############################################

=pod 

=item &BuildProblemStatisticsPage()

Main interface to problem statistics.

=cut

###############################################
###############################################
sub BuildProblemStatisticsPage {
    my ($r,$c)=@_;
    #
    $output_mode = 'html';
    $show = 'grouped';
    #
    $r->print(&CreateInterface());
    $r->print('<input type="hidden" name="statsfirstcall" value="no" />');
    $r->print('<input type="hidden" name="sortby" value="'.$ENV{'form.sortby'}.
              '" />');
    if (! exists($ENV{'form.statsfirstcall'})) {
        $r->print(<<ENDMSG);
<p>
<font size="+1">
Please make your selections in the boxes above and hit 
the button marked &quot;Update&nbsp;Display&quot;.
</font>
</p>
ENDMSG
        return;
    }
    #
    &Gather_Student_Data($r);
    #
    #
    if ($output_mode eq 'html') {
        $r->print("<h2>".
                  $ENV{'course.'.$ENV{'request.course.id'}.'.description'}.
                  "</h2>\n");
        $r->print("<h3>".localtime(time)."</h3>");
        $r->rflush();
        if ($show eq 'grouped') {
            &output_html_grouped_by_sequence($r);
        } elsif ($show eq 'ungrouped') {
            &output_html_ungrouped($r);
        }
    } elsif ($output_mode eq 'excel') {
        $r->print("<h2>Preparing Excel Spreadsheet</h2>");
        &output_excel($r);
    } elsif ($output_mode eq 'plot') {
        if ($show eq 'deg of diff') {
            &plot_statistics($r,'DoDiff');
        } elsif ($show eq 'per wrong') {
            &plot_statistics($r,'%Wrng');
        }
    } else {
        $r->print("<h1>Not implemented</h1>");
    }
    return;
}

###############################################
###############################################

=pod 

=item &output_html_grouped_by_sequence()

Presents the statistics data as an html table organized by the order
the assessments appear in the course.

=cut

###############################################
###############################################
sub output_html_grouped_by_sequence {
    my ($r) = @_;
    my $problem_num = 0;
    #$r->print(&ProblemStatisticsLegend());
    my @Header = ("Title","Part","#Stdnts","Tries","Mod",
                  "Mean","#YES","#yes","%Wrng","DoDiff",
                  "S.D.","Skew.");#,"D.F.1st","D.F.2nd");
    # #FFFFE6 #EEFFCC #DDFFFF FFDDDD #DDFFDD #FFDDFF
    foreach my $sequence (&Apache::lonstatistics::Sequences_with_Assess()) {
        next if ($sequence->{'num_assess'}<1);
        $r->print("<h3>".$sequence->{'title'}."</h3>");
        $r->print('<table border="0"><tr><td bgcolor="#777777">'."\n");
        $r->print('<table border="0" cellpadding="3">'."\n");
        $r->print('<tr bgcolor="#FFFFE6"><th>'.
                  join("</th><th>",@Header)."</th></tr>\n");
        foreach my $resource (@{$sequence->{'contents'}}) {
            next if ($resource->{'type'} ne 'assessment');
            foreach my $part (@{$resource->{'parts'}}) {
                $problem_num++;
                my ($num,$tries,$mod,$mean,$Solved,$solved,$DegOfDiff,$STD,
                    $SKEW) = &Apache::loncoursedata::get_problem_statistics
                        (undef,$resource->{'symb'},$part,
                         $ENV{'request.course.id'});
                #
                $part = '&nbsp;' if ($part == 0);
                #
                my $wrongpercent = 0;
                if (defined($num) && $num > 0) {
                    $wrongpercent=int(10*100*($num-$Solved+$solved)/$num)/10;
                }
                my $option = '';
                $r->print('<tr>'.&statistics_html_table_data
                          ($resource,$part,$num,$tries,$mod,$mean,$Solved,
                           $solved,$wrongpercent,$DegOfDiff,$STD,$SKEW,
                           $option).
                          "</tr>\n");
            }
        }
        $r->print("</table>\n");
        $r->print("</td></tr></table>\n");
        $r->rflush();
    }
    #
    return;
}

###############################################
###############################################

=pod 

=item &output_html_ungrouped()

Presents the statistics data in a single html table which can be sorted by
different columns.

=cut

###############################################
###############################################
sub output_html_ungrouped {
    my ($r,$option) = @_;
    #
    my $problem_num = 0;
    my $show_container = 0;
    my $show_part = 0;
    #$r->print(&ProblemStatisticsLegend());
    my @Header = ("Title","Part","#Stdnts","Tries","Mod",
                  "Mean","#YES","#yes","%Wrng","DoDiff",
                  "S.D.","Skew");#,"D.F.1st","D.F.2nd");
    #
    my $sortby = undef;
    foreach (@Header) {
        if ($ENV{'form.sortby'} eq $_) {
            $sortby = $_;
        }
    }
    if (! defined($sortby) || $sortby eq '') {
        $sortby = 'Container';
    }
    # If there is more than one sequence, list their titles
    my @Sequences = &Apache::lonstatistics::Sequences_with_Assess();
    if (@Sequences > 1) {
        unshift(@Header,"Container");
        $show_container = 1;
    }
    # 
    # If the option for showing the problem number is needed, push that
    # on the list too
    if (defined($option) && $option =~ /show probnum/) {
        unshift(@Header,"P#");
    }
    #
    $r->print('<table border="0"><tr><td bgcolor="#777777">'."\n");
    $r->rflush();
    #
    # Compile the data
    my @Statsarray;
    foreach my $sequence (@Sequences) {
        next if ($sequence->{'num_assess'}<1);
        foreach my $resource (@{$sequence->{'contents'}}) {
            next if ($resource->{'type'} ne 'assessment');
            foreach my $part (@{$resource->{'parts'}}) {
                $problem_num++;
                my ($num,$tries,$mod,$mean,$Solved,$solved,$DegOfDiff,$STD,
                    $SKEW) = &Apache::loncoursedata::get_problem_statistics
                        (undef,$resource->{'symb'},$part,
                         $ENV{'request.course.id'});
                #
                $show_part = 1 if ($part ne '0');
                $part = '&nbsp;' if ($part == 0);
                #
                my $wrongpercent = 0;
                if (defined($num) && $num > 0) {
                    $wrongpercent=int(10*100*($num-$Solved+$solved)/$num)/10;
                }
                push (@Statsarray,
                      { 'sequence' => $sequence,
                        'resource' => $resource,
                        'Title' => $resource->{'title'},
                        'Part'  => $part,
                        '#Stdnts' => $num,
                        'Tries' => $tries,
                        'Mod' => $mod,
                        'Mean' => $mean,
                        '#YES' => $Solved,
                        '#yes' => $solved,
                        '%Wrng' => $wrongpercent,
                        'DoDiff' => $DegOfDiff,
                        'S.D.' => $STD,
                        'Skew' => $SKEW,
                        'problem_num' => $problem_num,
                      });
            }
        }
    }
    #
    # Table Headers
    $r->print('<table border="0" cellpadding="3">'."\n");
    my $Str = '';
    foreach (@Header) {
        next if ($_ eq 'Part' && !$show_part);
        # Do not allow sorting on some fields
        if ($_ eq $sortby || /^(Part|P\#)$/) {  
            $Str .= '<th>'.$_.'</th>';
        } else {
            $Str .= '<th>'.
     '<a href="javascript:document.Statistics.sortby.value='."'$_'".
         ';document.Statistics.submit();">'.
             $_.'</a></th>';
        }
    }
    $r->print('<tr bgcolor="#FFFFE6">'.$Str."</tr>\n");
    #
    # Sort the data
    my @OutputOrder;
    if ($sortby eq 'Container') {
        @OutputOrder = @Statsarray;
    } else {
        # $sortby is already defined, so we can charge ahead
        if ($sortby =~ /^(title|part)$/i) {
            # Alpha comparison
            @OutputOrder = sort {
                lc($a->{$sortby}) cmp lc($b->{$sortby}) ||
                    lc($a->{'Title'}) cmp lc($b->{'Title'}) ||
                        lc($a->{'Part'}) cmp lc($b->{'Part'});
            } @Statsarray;
        } else {
            # Numerical comparison
            @OutputOrder = sort {
                my $retvalue = 0;
                if ($b->{$sortby} eq 'nan') {
                    if ($a->{$sortby} ne 'nan') {
                        $retvalue = -1;
                    } else {
                        $retvalue = 0;
                    }
                }
                if ($a->{$sortby} eq 'nan') {
                    if ($b->{$sortby} ne 'nan') {
                        $retvalue = 1;
                    }
                }
                if ($retvalue eq '0') {
                    $retvalue = $b->{$sortby} <=> $a->{$sortby} ||
                                lc($a->{'Title'}) <=> lc($b->{'Title'}) ||
                                lc($a->{'Part'})  <=> lc($b->{'Part'});
                }
                $retvalue;
            } @Statsarray;
        }
    }
    $option .= ',no part' if (! $show_part);
    foreach my $row (@OutputOrder) {
        $r->print('<tr>');
        if (defined($option) && $option =~ /show probnum/) {
            $r->print('<td bgcolor="#FFFFE6">'.$row->{'problem_num'}.'</td>');
        }
        if ($show_container) {
            $r->print('<td bgcolor="#FFFFE6">'
                      .$row->{'sequence'}->{'title'}.'</td>');
        }
        $r->print(&statistics_html_table_data
                  ($row->{'resource'},$row->{'Part'},$row->{'#Stdnts'},
                   $row->{'Tries'},$row->{'Mod'},$row->{'Mean'},
                   $row->{'#YES'},$row->{'#yes'},$row->{"\%Wrng"},
                   $row->{'DoDiff'},$row->{'S.D.'},$row->{'Skew'},
                   $option));
        $r->print("</tr>\n");
    }
    $r->print("</table>\n");
    $r->print("</td></tr></table>\n");
    $r->rflush();
    #
    return;
}

###############################################
###############################################

=pod 

=item &output_excel()

Presents the statistical data in an Excel 95 compatable spreadsheet file.

=cut

###############################################
###############################################
sub output_excel {
    my ($r) = @_;
    my $filename = '/prtspool/'.
        $ENV{'user.name'}.'_'.$ENV{'user.domain'}.'_'.
            time.'_'.rand(1000000000).'.xls';
    #
    my $excel_workbook = undef;
    my $excel_sheet = undef;
    #
    my $rows_output = 0;
    my $cols_output = 0;
    #
    # Create sheet
    $excel_workbook = Spreadsheet::WriteExcel->new('/home/httpd'.$filename);
    #
    # Check for errors
    if (! defined($excel_workbook)) {
        $r->log_error("Error creating excel spreadsheet $filename: $!");
        $r->print("Problems creating new Excel file.  ".
                  "This error has been logged.  ".
                  "Please alert your LON-CAPA administrator");
        return ;
    }
    #
    # The excel spreadsheet stores temporary data in files, then put them
    # together.  If needed we should be able to disable this (memory only).
    # The temporary directory must be specified before calling 'addworksheet'.
    # File::Temp is used to determine the temporary directory.
    $excel_workbook->set_tempdir($Apache::lonnet::tmpdir);
    #
    # Add a worksheet
    my $sheetname = $ENV{'course.'.$ENV{'request.course.id'}.'.description'};
    if (length($sheetname) > 31) {
        $sheetname = substr($sheetname,0,31);
    }
    $excel_sheet = $excel_workbook->addworksheet($sheetname);
    #
    # Put the course description in the header
    $excel_sheet->write($rows_output,$cols_output++,
                   $ENV{'course.'.$ENV{'request.course.id'}.'.description'});
    $cols_output += 3;
    #
    # Put a description of the sections listed
    my $sectionstring = '';
    my @Sections = @Apache::lonstatistics::SelectedSections;
    if (scalar(@Sections) > 1) {
        if (scalar(@Sections) > 2) {
            my $last = pop(@Sections);
            $sectionstring = "Sections ".join(', ',@Sections).', and '.$last;
        } else {
            $sectionstring = "Sections ".join(' and ',@Sections);
        }
    } else {
        if ($Sections[0] eq 'all') {
            $sectionstring = "All sections";
        } else {
            $sectionstring = "Section ".$Sections[0];
        }
    }
    $excel_sheet->write($rows_output,$cols_output++,$sectionstring);
    $cols_output += scalar(@Sections);
    #
    # Put the date in there too
    $excel_sheet->write($rows_output,$cols_output++,
                        'Compiled on '.localtime(time));
    #
    $rows_output++; 
    $cols_output=0;
    #
    # Add the headers
    my @Header = ("Container","Title","Part","#Stdnts","Tries","Mod",
                  "Mean","#YES","#yes","%Wrng","DoDiff",
                  "S.D.","Skew.");#,"D.F.1st","D.F.2nd");
    foreach (@Header) {
        $excel_sheet->write($rows_output,$cols_output++,$_);
    }
    $rows_output++;
    #
    # Write the data
    foreach my $sequence (&Apache::lonstatistics::Sequences_with_Assess()) {
        next if ($sequence->{'num_assess'}<1);
        foreach my $resource (@{$sequence->{'contents'}}) {
            next if ($resource->{'type'} ne 'assessment');
            foreach my $part (@{$resource->{'parts'}}) {
                $cols_output=0;
                my ($num,$tries,$mod,$mean,$Solved,$solved,$DegOfDiff,$STD,
                    $SKEW) = &Apache::loncoursedata::get_problem_statistics
                        (undef,$resource->{'symb'},$part,
                         $ENV{'request.course.id'});
                #
                if (!defined($part) || $part eq '') {
                    $part = ' ';
                }
                my $wrongpercent = 0;
                if (defined($num) && $num > 0) {
                    $wrongpercent=int(10*100*($num-$Solved+$solved)/$num)/10;
                }
                foreach ($sequence->{'title'},$resource->{'title'},$part,
                         $num,$tries,$mod,$mean,$Solved,$solved,$wrongpercent,
                         $DegOfDiff,$STD,$SKEW) {
                    $excel_sheet->write($rows_output,$cols_output++,$_);
                }
                $rows_output++;
            }
        }
    }
    #
    # Write the excel file
    $excel_workbook->close();
    # Tell the user where to get their excel file
    $r->print('<br />'.
              '<a href="'.$filename.'">Your Excel spreadsheet.</a>'."\n");
    $r->rflush();
    return;
}

###############################################
###############################################

=pod 

=item &statistics_html_table_data()

Help function used to format the rows for HTML table output.

=cut

###############################################
###############################################
sub statistics_html_table_data {
    my ($resource,$part,$num,$tries,$mod,$mean,$Solved,$solved,$wrongpercent,
        $DegOfDiff,$STD,$SKEW,$options) = @_;
    my $row = '';
    $row .= '<td bgcolor="#FFFFE6">'.
        '<a href="'.$resource->{'src'}.'" target="_blank" >'.
            $resource->{'title'}.'</a>'.
                '</td>';
    $row .= '<td bgcolor="#FFFFE6">'.$part.'</td>' if ($options !~ /no part/);
    foreach ($num,$tries) {
        $row .= '<td bgcolor="#EEFFCC" align="right">'.$_.'</td>';
    }
    foreach ($mod) {
        $row .= '<td bgcolor="#DDFFFF" align="right">'.$_.'</td>';
    }
    foreach ($mean) {
        $row .= '<td bgcolor="#DDFFFF" align="right">'.
                  sprintf("%5.2f",$_).'</td>';
    }
    foreach ($Solved,$solved) {
        $row .= '<td bgcolor="#DDFFFF" align="right">'.$_.'</td>';
    }
    foreach ($wrongpercent) {
        $row .= '<td bgcolor="#DDFFFF" align="right">'.
                  sprintf("%5.1f",$_).'</td>';
    }
    foreach ($DegOfDiff,$STD,$SKEW) {
        $row .= '<td bgcolor="#FFDDDD" align="right">'.
                  sprintf("%5.2f",$_).'</td>';
    }
    return $row;
}

###############################################
###############################################

=pod 

=item &plot_statistics()

=cut

###############################################
###############################################
sub plot_statistics {
    my ($r,$datafield) = @_;
    my @Data;
    #
    my %Fields = ('#Stdnts'=> 0,
                  'Tries'  => 1,
                  'Mod'    => 2,
                  'Mean'   => 3,
                  '#YES'   => 4,
                  '#yes'   => 5,
                  '%Wrng'  => 9,
                  'DoDiff' => 6,
                  'S.D.'   => 7,
                  'Skew'   => 8,);
    #
    my $field = '%Wrng';
    foreach (keys(%Fields)) {
        $field = $_ if ($datafield eq $_);
    }
    my $fieldindex = $Fields{$field};
    #
    my $Max = 0;
    foreach my $sequence (&Apache::lonstatistics::Sequences_with_Assess()) {
        next if ($sequence->{'num_assess'}<1);
        foreach my $resource (@{$sequence->{'contents'}}) {
            next if ($resource->{'type'} ne 'assessment');
            foreach my $part (@{$resource->{'parts'}}) {
                my @Results = &Apache::loncoursedata::get_problem_statistics
                        (undef,$resource->{'symb'},$part,
                         $ENV{'request.course.id'});
                my ($num,$Solved,$solved) = @Results[0,4,5];
                my $wrongpercent = 0;
                if (defined($num) && $num > 0) {
                    $wrongpercent=int(10*100*($num-$Solved+$solved)/$num)/10;
                }
                push (@Results,$wrongpercent);
                my $data = $Results[$fieldindex];
                $data = 0 if ($data eq 'nan');
                $Max = $data if ($Max<$data);
                push (@Data,$data);
            }
        }
    }
    #
    # Print out plot request
    my $title = 'Percent Wrong';
    if ($field eq 'DoDiff') {
        $title = 'Degree of Difficulty';
    }
    my $yaxis = 'Percent';
    if ($field eq 'DoDiff') {
        $yaxis = '';
    } elsif ($field ne '%Wrng') {
        $yaxis = '';
    }
    #
    # Determine appropriate value for $Max
    if ($field eq 'DoDiff') {
        if ($Max > 0.5) {
            $Max = 1;
        } elsif ($Max > 0.2) {
            $Max = 0.5;
        } elsif ($Max > 0.1) {
            $Max = 0.2;
        }
    } elsif ($field eq '%Wrng') {
        if ($Max > 50) {
            $Max = 100;
        } elsif ($Max > 25) {
            $Max = 50;
        } elsif ($Max > 20) {
            $Max = 25;
        } elsif ($Max > 10) {
            $Max = 20;
        } elsif ($Max > 5) {
            $Max = 10;
        } else {
            $Max = 5;
        }
    }
    
    $r->print("<p>".&DrawGraph(\@Data,$title,'Problem Number',$yaxis,
                               $Max)."</p>\n");
    #
    # Print out the data
    $ENV{'form.sortby'} = 'Contents';
    &output_html_ungrouped($r,'show probnum');
    return;
}

###############################################
###############################################

=pod 

=item &DrawGraph()

=cut

###############################################
###############################################
sub DrawGraph {
    my ($values,$title,$xaxis,$yaxis,$Max)=@_;
    $title = '' if (! defined($title));    
    $xaxis = '' if (! defined($xaxis));
    $yaxis = '' if (! defined($yaxis));
    #
    my $sendValues = join(',', @$values);
    my $sendCount = scalar(@$values);
    if ( $Max > 1 ) {
	if ($Max % 10) {
            if ( int($Max) < $Max ) {
	    	$Max++;
		$Max = int($Max);
	    }
	}
    } else { 
        $Max = 1; 
    }
    my @GData = ($title,$xaxis,$yaxis,$Max,$sendCount,$sendValues);
    return '<IMG src="/cgi-bin/graph.png?'.
        (join('&', @GData)).'" border="1" />';
}

###############################################
###############################################

=pod 

=item &ProblemStatisticsLegend()

=cut

###############################################
###############################################
sub ProblemStatisticsLegend {
    my $Ptr = '';
    $Ptr = '<table border="0">';
    $Ptr .= '<tr><td>';
    $Ptr .= '<b>#Stdnts</b></td>';
    $Ptr .= '<td>Total number of students attempted the problem.';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>Tries</b></td>';
    $Ptr .= '<td>Total number of tries for solving the problem.';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>Mod</b></td>';
    $Ptr .= '<td>Largest number of tries for solving the problem by a student.';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>Mean</b></td>';
    $Ptr .= '<td>Average number of tries. [ Tries / #Stdnts ]';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>#YES</b></td>';
    $Ptr .= '<td>Number of students solved the problem correctly.';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>#yes</b></td>';
    $Ptr .= '<td>Number of students solved the problem by override.';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>%Wrong</b></td>';
    $Ptr .= '<td>Percentage of students who tried to solve the problem ';
    $Ptr .= 'but is still incorrect. [ 100*((#Stdnts-(#YES+#yes))/#Stdnts) ]';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>DoDiff</b></td>';
    $Ptr .= '<td>Degree of Difficulty of the problem.  ';
    $Ptr .= '[ 1 - ((#YES+#yes) / Tries) ]';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>S.D.</b></td>';
    $Ptr .= '<td>Standard Deviation of the tries.  ';
    $Ptr .= '[ sqrt(sum((Xi - Mean)^2)) / (#Stdnts-1) ';
    $Ptr .= 'where Xi denotes every student\'s tries ]';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>Skew.</b></td>';
    $Ptr .= '<td>Skewness of the students tries.';
    $Ptr .= '[(sqrt( sum((Xi - Mean)^3) / #Stdnts)) / (S.D.^3)]';
    $Ptr .= '</td></tr><tr><td>';
    $Ptr .= '<b>Dis.F.</b></td>';
    $Ptr .= '<td>Discrimination Factor: A Standard for evaluating the ';
    $Ptr .= 'problem according to a Criterion<br>';
    $Ptr .= '<b>[Criterion to group students into %27 Upper Students - ';
    $Ptr .= 'and %27 Lower Students]</b><br>';
    $Ptr .= '<b>1st Criterion</b> for Sorting the Students: ';
    $Ptr .= '<b>Sum of Partial Credit Awarded / Total Number of Tries</b><br>';
    $Ptr .= '<b>2nd Criterion</b> for Sorting the Students: ';
    $Ptr .= '<b>Total number of Correct Answers / Total Number of Tries</b>';
    $Ptr .= '</td></tr>';
    $Ptr .= '<tr><td><b>Disc.</b></td>';
    $Ptr .= '<td>Number of Students had at least one discussion.';
    $Ptr .= '</td></tr></table>';
    return $Ptr;
}

#---- END Problem Statistics Web Page ----------------------------------------

1;
__END__