".&Apache::loncommon::DrawBarGraph($title,
+ 'Problem Number',
+ $yaxis,
+ $max,
+ undef, # colors
+ \@Labels,
+ \@Data)."
\n");
+ return;
}
-sub BuildStatisticsTable {
- my ($cache,$displayFormat,$sortProblems,$orderedProblems,$headings,
- $r,$color)=@_;
-
- my $count = 1;
- my $currentSequence = -1;
- foreach(@$orderedProblems) {
- my ($sequence,$problem,$part)=split(':', $_);
- if($cache->{'StatisticsMaps'} ne 'All Maps' &&
- $cache->{'StatisticsMaps'} ne $cache->{$sequence.':title'}) {
- next;
+sub degrees_plot {
+ my ($r)=@_;
+ my $count = scalar(@StatsArray);
+ my $width = 50 + 10*$count;
+ $width = 300 if ($width < 300);
+ my $height = 300;
+ my $plot = '';
+ my $ymax = 0;
+ my $ymin = 0;
+ my @Disc; my @Diff; my @Labels;
+ foreach my $data (@StatsArray) {
+ push(@Labels,$data->{'problem_num'});
+ my $disc = $data->{'deg_of_disc'};
+ my $diff = $data->{'deg_of_diff'};
+ push(@Disc,$disc);
+ push(@Diff,$diff);
+ #
+ $ymin = $disc if ($ymin > $disc);
+ $ymin = $diff if ($ymin > $diff);
+ $ymax = $disc if ($ymax < $disc);
+ $ymax = $diff if ($ymax < $diff);
+ }
+ #
+ # Make sure we show relevant information.
+ if ($ymin < 0) {
+ if (abs($ymin) < 0.05) {
+ $ymin = 0;
+ } else {
+ $ymin = -1;
}
-
- if($currentSequence == -1 ||
- ($sortProblems eq 'Sort Within Sequence' &&
- $currentSequence != $sequence)) {
- if($displayFormat ne 'Display CSV Format') {
- if($currentSequence ne -1) {
- $r->print('');
- $r->print(''."\n");
- $r->print(''."\n");
- $r->print(&CreateProblemStatisticsTableHeading($headings, $r));
- } else {
- if($sortProblems eq 'Sort Within Sequence') {
- $r->print('"'.$cache->{$sequence.':title'}.'"');
- }
- $r->print(''.$cache->{$problem.':title'}.' ';
- my $title = $cache->{$problem.':title'};
- if($part != 0) {
- $title .= ' Part '.$part;
- }
- my $source = $cache->{$problem.':source'};
- my $tableData = join('&', $ref, $title, $source,
- $cache->{$_.':studentCount'},
- $cache->{$_.':totalTries'},
- $cache->{$_.':maxTries'},
- $cache->{$_.':mean'},
- $cache->{$_.':correct'},
- $cache->{$_.':correctByOverride'},
- $cache->{$_.':percentWrong'},
- $cache->{$_.':degreeOfDifficulty'},
- $cache->{$_.':standardDeviation'},
- $cache->{$_.':skewness'},
- $cache->{$_.':discriminationFactor1'},
- $cache->{$_.':discriminationFactor2'});
-
- &TableRow($displayFormat,$tableData,$count,$r,$color);
-
- $count++;
- }
- if($displayFormat ne 'Display CSV Format') {
- $r->print('
'."\n");
- $r->print('
');
} else {
- $r->print('';
- $Ptr .= '';
+ $Str .= 'none '."\n";
+ foreach my $field (@Fields,@Additional_Plots) {
+ if (! exists($field->{'graphable'}) ||
+ $field->{'graphable'} ne 'yes') {
+ next;
+ }
+ $Str .= '{'name'} eq $current) {
+ $Str .= ' selected ';
+ }
+ $Str.= '>'.&mt($field->{'title'}).' '."\n";
}
- $Ptr .= ' ';
- $Ptr .= ''.&mt('Preparing Excel Spreadsheet').' ');
+ ##
+ ## Compute the statistics
+ &compute_all_statistics($r);
+ my $c = $r->connection;
+ return if ($c->aborted());
+ ##
+ ## Create the excel workbook
+ my $filename = '/prtspool/'.
+ $ENV{'user.name'}.'_'.$ENV{'user.domain'}.'_'.
+ time.'_'.rand(1000000000).'.xls';
+ my ($starttime,$endtime) = &Apache::lonstathelpers::get_time_limits();
+ #
+ # Create sheet
+ my $excel_workbook = Spreadsheet::WriteExcel->new('/home/httpd'.$filename);
+ #
+ # Check for errors
+ if (! defined($excel_workbook)) {
+ $r->log_error("Error creating excel spreadsheet $filename: $!");
+ $r->print(&mt("Problems creating new Excel file. ".
+ "This error has been logged. ".
+ "Please alert your LON-CAPA administrator."));
+ return 0;
+ }
+ #
+ # 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);
+ }
+ my $excel_sheet = $excel_workbook->addworksheet(
+ &Apache::loncommon::clean_excel_name($sheetname));
+ ##
+ ## Begin creating excel sheet
+ ##
+ my ($rows_output,$cols_output) = (0,0);
+ #
+ # 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 {
- $Ptr .= 'value="Show Legend" />'."\n";
+ if ($Sections[0] eq 'all') {
+ $sectionstring = "All sections";
+ } else {
+ $sectionstring = "Section ".$Sections[0];
+ }
}
- $Ptr .= ' ';
- $Ptr .= ' ';
- $Ptr .= '';
- $Ptr .= '#Stdnts ';
- $Ptr .= 'Total number of students attempted the problem.';
- $Ptr .= ' ';
- $Ptr .= 'Tries ';
- $Ptr .= 'Total number of tries for solving the problem.';
- $Ptr .= ' ';
- $Ptr .= 'Mod ';
- $Ptr .= 'Largest number of tries for solving the problem by a student.';
- $Ptr .= ' ';
- $Ptr .= 'Mean ';
- $Ptr .= 'Average number of tries. [ Tries / #Stdnts ]';
- $Ptr .= ' ';
- $Ptr .= '#YES ';
- $Ptr .= 'Number of students solved the problem correctly.';
- $Ptr .= ' ';
- $Ptr .= '#yes ';
- $Ptr .= 'Number of students solved the problem by override.';
- $Ptr .= ' ';
- $Ptr .= '%Wrong ';
- $Ptr .= 'Percentage of students who tried to solve the problem ';
- $Ptr .= 'but is still incorrect. [ 100*((#Stdnts-(#YES+#yes))/#Stdnts) ]';
- $Ptr .= ' ';
- $Ptr .= 'DoDiff ';
- $Ptr .= 'Degree of Difficulty of the problem. ';
- $Ptr .= '[ 1 - ((#YES+#yes) / Tries) ]';
- $Ptr .= ' ';
- $Ptr .= 'S.D. ';
- $Ptr .= 'Standard Deviation of the tries. ';
- $Ptr .= '[ sqrt(sum((Xi - Mean)^2)) / (#Stdnts-1) ';
- $Ptr .= 'where Xi denotes every student\'s tries ]';
- $Ptr .= ' ';
- $Ptr .= 'Skew. ';
- $Ptr .= 'Skewness of the students tries.';
- $Ptr .= '[(sqrt( sum((Xi - Mean)^3) / #Stdnts)) / (S.D.^3)]';
- $Ptr .= ' ';
- $Ptr .= 'Dis.F. ';
- $Ptr .= 'Discrimination Factor: A Standard for evaluating the ';
- $Ptr .= 'problem according to a Criterion[Criterion to group students into %27 Upper Students - ';
- $Ptr .= 'and %27 Lower Students] 1st Criterion for Sorting the Students: ';
- $Ptr .= 'Sum of Partial Credit Awarded / Total Number of Tries 2nd Criterion for Sorting the Students: ';
- $Ptr .= 'Total number of Correct Answers / Total Number of Tries ';
- $Ptr .= ' Disc. Number of Students had at least one discussion.';
- $Ptr .= '
';
-
- return $Ptr;
-}
-
-sub ExtractStudentData {
- my ($cache, $students)=@_;
-
- my @problemList=();
- my %problemData;
- foreach my $sequence (split(':', $cache->{'orderedSequences'})) {
- foreach my $problemID (split(':', $cache->{$sequence.':problems'})) {
- foreach my $part (split(/\:/,$cache->{$sequence.':'.
- $problemID.
- ':parts'})) {
- my $id = $sequence.':'.$problemID.':'.$part;
- push(@problemList, $id);
- my $totalTries = 0;
- my $totalAwarded = 0;
- my $correct = 0;
- my $correctByOverride = 0;
- my $studentCount = 0;
- my $maxTries = 0;
- my $totalFirst = 0;
- my @studentTries=();
- foreach(@$students) {
- my $code = $cache->{"$_:$problemID:$part:code"};
-
- if(defined($cache->{$_.':error'}) || $code eq ' ' ||
- $cache->{"$_:$problemID:NoVersion"} eq 'true') {
- next;
- }
+sub compute_all_statistics {
+ my ($r) = @_;
+ if (@StatsArray > 0) {
+ # Assume we have already computed the statistics
+ return;
+ }
+ my $c = $r->connection;
+ foreach my $seq (&Apache::lonstatistics::Sequences_with_Assess()) {
+ last if ($c->aborted);
+ next if ($seq->{'num_assess'} < 1);
+ &compute_statistics_on_sequence($seq);
+ }
+}
- $studentCount++;
- my $tries = $cache->{"$_:$problemID:$part:tries"};
- if($maxTries < $tries) {
- $maxTries = $tries;
+sub sort_data {
+ my ($sortkey) = @_;
+ return if (! @StatsArray);
+ #
+ # Sort the data
+ my $sortby = undef;
+ foreach my $field (@Fields) {
+ if ($sortkey eq $field->{'name'}) {
+ $sortby = $field->{'name'};
+ }
+ }
+ if (! defined($sortby) || $sortby eq '' || $sortby eq 'problem_num') {
+ $sortby = 'container';
+ }
+ if ($sortby ne 'container') {
+ # $sortby is already defined, so we can charge ahead
+ if ($sortby =~ /^(title|part)$/i) {
+ # Alpha comparison
+ @StatsArray = sort {
+ lc($a->{$sortby}) cmp lc($b->{$sortby}) ||
+ lc($a->{'title'}) cmp lc($b->{'title'}) ||
+ lc($a->{'part'}) cmp lc($b->{'part'});
+ } @StatsArray;
+ } else {
+ # Numerical comparison
+ @StatsArray = sort {
+ my $retvalue = 0;
+ if ($b->{$sortby} eq 'nan') {
+ if ($a->{$sortby} ne 'nan') {
+ $retvalue = -1;
+ } else {
+ $retvalue = 0;
}
- $totalTries += $tries;
- push(@studentTries, $tries);
-
- my $awarded = $cache->{"$_:$problemID:$part:awarded"};
- $totalAwarded += $awarded;
-
- if($code eq '*') {
- $correct++;
- if($tries == 1) {
- $totalFirst++;
- }
- } elsif($code eq '+') {
- $correctByOverride++;
+ }
+ if ($a->{$sortby} eq 'nan') {
+ if ($b->{$sortby} ne 'nan') {
+ $retvalue = 1;
}
}
-
- my $studentTriesJoined = join(':::', @studentTries);
- $problemData{$id.':sequenceTitle'} =
- $cache->{$sequence.':title'};
- $problemData{$id.':studentCount'} = $studentCount;
- $problemData{$id.':totalTries'} = $totalTries;
- $problemData{$id.':studentTries'} = $studentTriesJoined;
- $problemData{$id.':totalAwarded'} = $totalAwarded;
- $problemData{$id.':correct'} = $correct;
- $problemData{$id.':correctByOverride'} = $correctByOverride;
- $problemData{$id.':wrong'} = $studentCount -
- ($correct + $correctByOverride);
- $problemData{$id.':maxTries'} = $maxTries;
- $problemData{$id.':totalFirst'} = $totalFirst;
- }
+ if ($retvalue eq '0') {
+ $retvalue = $b->{$sortby} <=> $a->{$sortby} ||
+ lc($a->{'title'}) <=> lc($b->{'title'}) ||
+ lc($a->{'part'}) <=> lc($b->{'part'});
+ }
+ $retvalue;
+ } @StatsArray;
}
}
-
- my @upperStudents1=();
- my @lowerStudents1=();
- my @upperStudents2=();
- my @lowerStudents2=();
- my $upperCount = int(0.27*scalar(@$students));
- # Discriminant Factor criterion 1
- my $sortedStudents = &SortDivideByTries($students,$cache,':totalAwarded');
-
- for(my $i=0; $i<$upperCount; $i++) {
- push(@lowerStudents1, $sortedStudents->[$i]);
- push(@upperStudents1, $sortedStudents->[(scalar(@$students)-$i-1)]);
- }
-
- $problemData{'studentsUpperListCriterion1'}=join(':::', @upperStudents1);
- $problemData{'studentsLowerListCriterion1'}=join(':::', @lowerStudents1);
-
- # Discriminant Factor criterion 2
- $sortedStudents = &SortDivideByTries($students, $cache, ':totalSolved');
-
- for(my $i=0; $i<$upperCount; $i++) {
- push(@lowerStudents2, $sortedStudents->[$i]);
- push(@upperStudents2, $sortedStudents->[(scalar(@$students)-$i-1)]);
- }
- $problemData{'studentsUpperListCriterion2'}=join(':::', @upperStudents2);
- $problemData{'studentsLowerListCriterion2'}=join(':::', @lowerStudents2);
-
- $problemData{'problemList'} = join(':::', @problemList);
-
- return \%problemData;
-}
-
-sub SortDivideByTries {
- my ($toSort, $data, $sortOn)=@_;
- my @orderedData = sort { ($data->{$a.':totalTries'}) ?
- ($data->{$a.$sortOn}/$data->{$a.':totalTries'}):0
- <=>
- ($data->{$b.':totalTries'}) ?
- ($data->{$b.$sortOn}/$data->{$b.':totalTries'}):0
- } @$toSort;
-
- return \@orderedData;
-}
-
-sub SortProblems {
- my ($problemData,$sortBy,$sortProblems,$ascend)=@_;
-
- my @problems = split(':::', $problemData->{'problemList'});
- if($sortBy eq "Homework Sets Order") {
- return \@problems;
- }
-
- my $data;
-
- if ($sortBy eq "#Stdnts") { $data = ':studentCount'; }
- elsif($sortBy eq "Tries") { $data = ':totalTries'; }
- elsif($sortBy eq "Mod") { $data = ':maxTries'; }
- elsif($sortBy eq "Mean") { $data = ':mean'; }
- elsif($sortBy eq "#YES") { $data = ':correct'; }
- elsif($sortBy eq "#yes") { $data = ':correctByOverride'; }
- elsif($sortBy eq "%Wrng") { $data = ':percentWrong'; }
- elsif($sortBy eq "DoDiff") { $data = ':degreeOfDifficulty'; }
- elsif($sortBy eq "S.D.") { $data = ':standardDeviation'; }
- elsif($sortBy eq "Skew.") { $data = ':skewness'; }
- elsif($sortBy eq "D.F.1st") { $data = ':discriminationFactor1'; }
- elsif($sortBy eq "D.F.2nd") { $data = ':discriminationFactor2'; }
- else { return \@problems; }
-
- my %temp;
- my @sequenceList=();
- foreach(@problems) {
- my ($sequence) = split(':', $_);
-
- my @array=();
- my $tempArray;
- if(defined($temp{$sequence})) {
- $tempArray = $temp{$sequence};
- } else {
- push(@sequenceList, $sequence);
- $tempArray = \@array;
- $temp{$sequence} = $tempArray;
- }
-
- push(@$tempArray, $_);
- }
-
- my @orderedProblems;
- if($sortProblems eq "Sort Within Sequence") {
- foreach(keys(%temp)) {
- my $tempArray = $temp{$_};
- my @tempOrder =
- sort { $problemData->{$a.$data} <=> $problemData->{$b.$data} }
- @$tempArray;
- $temp{$_} = \@tempOrder;
- }
- foreach(@sequenceList) {
- my $tempArray = $temp{$_};
- @orderedProblems = (@orderedProblems, @$tempArray);
- }
- } else {
- @orderedProblems =
- sort { $problemData->{$a.$data} <=> $problemData->{$b.$data} }
- @problems;
+ #
+ # Renumber the data set
+ my $count;
+ foreach my $data (@StatsArray) {
+ $data->{'problem_num'} = ++$count;
}
+ return;
+}
- if($ascend eq 'Descending') {
- @orderedProblems = reverse(@orderedProblems);
- }
+########################################################
+########################################################
- return \@orderedProblems;
-}
+=pod
-sub CalculateStatistics {
- my ($data, $cache, $courseID)=@_;
+=item &get_statistics()
- my @problems = split(':::', $data->{'problemList'});
- foreach(@problems) {
- # Mean
- my $mean = ($data->{$_.':studentCount'}) ?
- ($data->{$_.':totalTries'} / $data->{$_.':studentCount'}) : 0;
- $data->{$_.':mean'} = sprintf("%.2f", $mean);
+Wrapper routine from the call to loncoursedata::get_problem_statistics.
+Calls lonstathelpers::get_time_limits() to limit the data set by time
+and &compute_discrimination_factor
+
+Inputs: $sequence, $resource, $part, $problem_num
+
+Returns: Hash reference with statistics data from
+loncoursedata::get_problem_statistics.
+
+=cut
+
+########################################################
+########################################################
+sub get_statistics {
+ my ($sequence,$resource,$part,$problem_num) = @_;
+ #
+ my ($starttime,$endtime) = &Apache::lonstathelpers::get_time_limits();
+ my $symb = $resource->{'symb'};
+ my $courseid = $ENV{'request.course.id'};
+ #
+ my $data = &Apache::loncoursedata::get_problem_statistics
+ (\@Apache::lonstatistics::SelectedSections,
+ $Apache::lonstatistics::enrollment_status,
+ $symb,$part,$courseid,$starttime,$endtime);
+ $data->{'part'} = $part;
+ $data->{'problem_num'} = $problem_num;
+ $data->{'container'} = $sequence->{'title'};
+ $data->{'title'} = $resource->{'title'};
+ $data->{'title.link'} = $resource->{'src'}.'?symb='.
+ &Apache::lonnet::escape($resource->{'symb'});
+ #
+ $data->{'deg_of_disc'} = &compute_discrimination_factor($resource,$part,$sequence);
+ return $data;
+}
- # %Wrong
- my $pw = ($data->{$_.':studentCount'}) ?
- (($data->{$_.':wrong'} / $data->{$_.':studentCount'}) * 100.0) :
- 100.0;
- $data->{$_.':percentWrong'} = sprintf("%.1f", $pw);
- # Degree of Difficulty
- my $dod = ($data->{$_.':totalTries'}) ?
- (1 - (($data->{$_.':correct'} + $data->{$_.':correctByOverride'}) /
- $data->{$_.':totalTries'})) : 0;
+###############################################
+###############################################
- $data->{$_.':degreeOfDifficulty'} = sprintf("%.2f", $dod);
+=pod
- # Factor in mean
- my @studentTries = split(':::', $data->{$_.':studentTries'});
- foreach(my $index=0; $index < scalar(@studentTries); $index++) {
- $studentTries[$index] -= $mean;
- }
- my $sumSquared = 0;
- my $sumCubed = 0;
- foreach(@studentTries) {
- my $squared = ($_ * $_);
- my $cubed = ($squared * $_);
- $sumSquared += $squared;
- $sumCubed += $cubed;
- }
+=item &compute_discrimination_factor()
- # Standard deviation
- my $standardDeviation;
- if($data->{$_.':studentCount'} - 1 > 0) {
- $standardDeviation = (sqrt($sumSquared)) /
- ($data->{$_.':studentCount'} - 1);
- } else {
- $standardDeviation = 0.0;
- }
- $data->{$_.':standardDeviation'} = sprintf("%.1f", $standardDeviation);
+Inputs: $Resource, $Sequence
- # Skewness
- my $skew;
- if($standardDeviation > 0.0999 && $data->{$_.':studentCount'} > 0) {
- $skew = (((sqrt($sumSquared)) / $data->{$_.':studentCount'}) /
- ($standardDeviation *
- $standardDeviation *
- $standardDeviation));
- } else {
- $skew = 0.0;
- }
+Returns: integer between -1 and 1
+
+=cut
+
+###############################################
+###############################################
+sub compute_discrimination_factor {
+ my ($resource,$part,$sequence) = @_;
+ my @Resources;
+ foreach my $res (@{$sequence->{'contents'}}) {
+ next if ($res->{'symb'} eq $resource->{'symb'});
+ push (@Resources,$res->{'symb'});
+ }
+ #
+ # rank
+ my $ranking =
+ &Apache::loncoursedata::rank_students_by_scores_on_resources
+ (\@Resources,
+ \@Apache::lonstatistics::SelectedSections,
+ $Apache::lonstatistics::enrollment_status,undef);
+ #
+ # compute their percent scores on the problems in the sequence,
+ my $number_to_grab = int(scalar(@{$ranking})/4);
+ my $num_students = scalar(@{$ranking});
+ my @BottomSet = map { $_->[&Apache::loncoursedata::RNK_student()];
+ } @{$ranking}[0..$number_to_grab];
+ my @TopSet =
+ map {
+ $_->[&Apache::loncoursedata::RNK_student()];
+ } @{$ranking}[($num_students-$number_to_grab)..($num_students-1)];
+ my ($bottom_sum,$bottom_max) =
+ &Apache::loncoursedata::get_sum_of_scores($resource,$part,\@BottomSet);
+ my ($top_sum,$top_max) =
+ &Apache::loncoursedata::get_sum_of_scores($resource,$part,\@TopSet);
+ my $deg_of_disc;
+ if ($top_max == 0 || $bottom_max==0) {
+ $deg_of_disc = 'nan';
+ } else {
+ $deg_of_disc = ($top_sum/$top_max) - ($bottom_sum/$bottom_max);
+ }
+ #&Apache::lonnet::logthis(' '.$top_sum.'/'.$top_max.
+ # ' - '.$bottom_sum.'/'.$bottom_max);
+ return $deg_of_disc;
+}
- $data->{$_.':skewness'} = sprintf("%.1f", $skew);
+###############################################
+###############################################
- # Discrimination Factor 1
- my ($sequence, $problem, $part) = split(':', $_);
+=pod
- my @upper1 = split(':::', $data->{'studentsUpperListCriterion1'});
- my @lower1 = split(':::', $data->{'studentsLowerListCriterion1'});
+=item ProblemStatisticsLegend
- my $upper1Sum=0;
- foreach my $name (@upper1) {
- $upper1Sum += $cache->{"$name:$problem:$part:awarded"};
- }
- $upper1Sum = (scalar(@upper1)) ? ($upper1Sum/(scalar(@upper1))) : 0;
+=over 4
- my $lower1Sum=0;
- foreach my $name (@lower1) {
- $lower1Sum += $cache->{"$name:$problem:$part:awarded"};
- }
- $lower1Sum = (scalar(@lower1)) ? ($lower1Sum/(scalar(@lower1))) : 0;
+=item #Stdnts
+Total number of students attempted the problem.
+
+=item Tries
+Total number of tries for solving the problem.
+
+=item Max Tries
+Largest number of tries for solving the problem by a student.
+
+=item Mean
+Average number of tries. [ Tries / #Stdnts ]
+
+=item #YES
+Number of students solved the problem correctly.
+
+=item #yes
+Number of students solved the problem by override.
+
+=item %Wrong
+Percentage of students who tried to solve the problem
+but is still incorrect. [ 100*((#Stdnts-(#YES+#yes))/#Stdnts) ]
+
+=item DoDiff
+Degree of Difficulty of the problem.
+[ 1 - ((#YES+#yes) / Tries) ]
+
+=item S.D.
+Standard Deviation of the tries.
+[ sqrt(sum((Xi - Mean)^2)) / (#Stdnts-1)
+where Xi denotes every student\'s tries ]
+
+=item Skew.
+Skewness of the students tries.
+[(sqrt( sum((Xi - Mean)^3) / #Stdnts)) / (S.D.^3)]
+
+=item Dis.F.
+Discrimination Factor: A Standard for evaluating the
+problem according to a Criterion).')
');
-# $r->print('