########################################################################
## DESCRIPTION
## A WeBWorK problem that asks students to construct a frequency distribution 
## table and answer questions on it.
## WeBWorK problem written by JoAnne Taormina, <joanne(dot)taormina(at)ncc(dot)edu>
## ENDDESCRIPTION
##
## KEYWORDS('frequency distribution table')
##
## Author('JoAnne Taormina')
## Institution('Nassau Community College')
########################################################################

DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGgraphmacros.pl",
"PGchoicemacros.pl",
"unionTables.pl",
"weightedGrader.pl",
);
install_weighted_grader();

$refreshCachedImages=1;

# make sure we're in the context we want
Context("Numeric");

# the data
@data = ();
@sorted = ();
for($i = 0; $i < 40; $i ++)
{
  $data[$i] = random(100, 150, 1);
}
@sorted = num_sort(@data); 

# number of classes
$numclasses = 8;

# the table data
$table_start = begintable(5);
$table_row[0]  = row( "Classes", "Frequencies", "Class Marks", "Class Boundaries" , "Relative Percentages");

for ( $i = 1; $i <=$numclasses; $i++ )
{
   $table_row[$i]  = row( ans_rule(5) . "-" . ans_rule(5), ans_rule(10), ans_rule(10), ans_rule(5) . "-" . ans_rule(5), ans_rule(19) . "%" );
}
$table_end   = endtable();

$smallest = $sorted[0];
$largest = $sorted[39];
if(($largest - $smallest)%$numclasses==0)
{
  $class_width = ceil(( $largest - $smallest )/$numclasses) + 1;
}
else
{
  $class_width = ceil(( $largest - $smallest )/$numclasses);
}

TEXT(beginproblem());
Context()->texStrings;
BEGIN_TEXT
(a) Create a frequency distribution table with $BBOLD 8 classes $EBOLD from the following data.
$BR$BR
Include classes, frequencies, class marks, class boundaries, and relative percentages.  
$BR$BR
Relative percentages should be expressed as percents $BBOLD but do not put a % symbol in your answer or you will be marked wrong.$EBOLD  For example, 12.25 should be entered instead of 12.25%. Do not round any quantities.
$BR $BR
\[ $data[0], \ $data[1], \ $data[2], \ $data[3], \ $data[4], \ $data[5], \ $data[6], \ $data[7], \ $data[8], \ $data[9] \] 
\[ $data[10], \ $data[11], \ $data[12], \ $data[13], \ $data[14], \ $data[15], \ $data[16], \ $data[17], \ $data[18], \ $data[19] \] 
\[ $data[20], \ $data[21], \ $data[22], \ $data[23], \ $data[24], \ $data[25], \ $data[26], \ $data[27], \ $data[28], \ $data[29] \]
\[ $data[30], \ $data[31], \ $data[32], \ $data[33], \ $data[34], \ $data[35], \ $data[36], \ $data[37], \ $data[38], \ $data[39] \]
$BR $BR
$BCENTER

$table_start
$table_row[0]
$table_row[1]
$table_row[2]
$table_row[3]
$table_row[4]
$table_row[5]
$table_row[6]
$table_row[7]
$table_row[8]
$table_end

$ECENTER
END_TEXT

Context()->normalStrings;

for ($j=0; $j<$numclasses; $j++)
{
 $lower_limit = $smallest + $class_width*$j;
 $class_low_limit = Formula("$lower_limit");
 WEIGHTED_ANS( $class_low_limit->cmp(),1.5179 );

 $upper_limit = $lower_limit+$class_width-1;
 $class_high_limit = Formula("$upper_limit");
 WEIGHTED_ANS( $class_high_limit->cmp(),1.5179 );

 for ($k=0; $k<40; $k++){
   if($data[$k]>=$lower_limit && $data[$k]<=$upper_limit){
     $frequency++;
   }
 }
 $class_frequency = Formula("$frequency");
 WEIGHTED_ANS ($class_frequency->cmp(),1.5179);

 $class_mark = ($lower_limit + $upper_limit) / 2;
 $class_mark = Formula("$class_mark");
 WEIGHTED_ANS ($class_mark->cmp(),1.5179);

 $lower_class_boundary = $lower_limit - .5;
 $class_boundary_low = Formula("$lower_class_boundary");
 WEIGHTED_ANS($class_boundary_low->cmp(),1.5179);

 if($j == 2){
  $start_part_b = $lower_limit;
 }
 if($j==3){
  $start_part_c = $lower_limit;
 }
 $upper_class_boundary = $upper_limit + .5;
 $class_boundary_high = Formula("$upper_class_boundary");
 WEIGHTED_ANS( $class_boundary_high->cmp(),1.5179);

 if($j == 5){
  $end_part_b = $upper_limit;
 }
 if($j==4){
  $end_part_d = $upper_limit;
 }   

 $relative_percentage = ($frequency / 40)*100;
 if($j>=3){
  $answer_part_c+=$relative_percentage;
 }
 if($j>=2 && $j<=5){
   $answer_part_b+=$relative_percentage;
 }
 if($j<=4){
   $answer_part_d+=$relative_percentage;
 }
 $relative_percentage = Formula("$relative_percentage");
 WEIGHTED_ANS($relative_percentage->cmp(),1.5179);  
 $frequency = 0;
}
$answer_part_b = Formula("$answer_part_b");
WEIGHTED_ANS($answer_part_b->cmp(),5);
$answer_part_c = Formula("$answer_part_c");
WEIGHTED_ANS($answer_part_c->cmp(),5);
$answer_part_d = Formula("$answer_part_d");
WEIGHTED_ANS($answer_part_d->cmp(),5);

BEGIN_TEXT
$BR$BR
(b) What is the percentage of data values that fall between \{ $start_part_b \} and \{ $end_part_b \}, inclusive? $BITALIC Express your answer as a percent without the % symbol. $EITALIC
\{ans_rule(5)\}% 
$BR$BR
(c) What is the percentage of data values are \{ $start_part_c \} or greater? $BITALIC Express your answer as a percent without the % symbol. $EITALIC
\{ans_rule(5)\}% 
$BR$BR
(d) What is the percentage of data values that are \{ $end_part_d \} or less? $BITALIC Express your answer as a percent without the % symbol. $EITALIC
$BR
\{ans_rule(5)\}% 
$ECENTER

$BR$BR

END_TEXT

ENDDOCUMENT();