# DESCRIPTION
# Interpreting a histogram - three examples
# Output controlled by contents of @case
# WeBWorK problem written by Hedley Pinsent, 
# <hedley.pinsent(at)cna(dot)nl >
# ENDDESCRIPTION

## DBsubject('WeBWorK')
## DBchapter('Statistics')
## DBsection('Grouped Data')
## KEYWORDS('')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')
## Author('Hedley Pinsent')
## Institution('College of the North Atlantic')

DOCUMENT();
loadMacros(
   "PGstandard.pl",     # Standard macros for PG language
   "MathObjects.pl",
"PGchoicemacros.pl",
"PGgraphmacros.pl"
);
$showPartialCorrectAnswers = 1;
$refreshCachedImages = 1;
$trial =0;
#@caselist = (0,1,2);
@caselist = list_random(0,1,2);

foreach $case (@caselist){
$trial += 1;
if ($case ==0){
#Starting Parameters VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV
$ClassInterval = list_random(2,5,10);
$MidLowest = random(10,30,5);
$NumberClasses = list_random(4,5,6);
$n = random(int(2**($NumberClasses-1)),int(2**$NumberClasses-1), 1);
@probabilityPattern = ();
push  @probabilityPattern , 0..$NumberClasses-1;
push  @probabilityPattern , 1..$NumberClasses-2; #for a central preference

}  #end of case 0

# case = 1 (student marks)
if ($case ==1){
#Starting Parameters VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV
$ClassInterval = list_random(5,10);
#$MidLowest = random(10,30,5);
$NumberClasses = list_random(4,5,6);
$MidLowest = list_random(80,90,100) - ($NumberClasses -0.5)*$ClassInterval;
$n = random(int(2**($NumberClasses-1)),int(2**$NumberClasses-1), 1);
@probabilityPattern = ();
push  @probabilityPattern , 0..$NumberClasses-1;
push  @probabilityPattern , 1..$NumberClasses-2; #for a central preference

}  #end of case 1

# case = 2 (active ingredients - decomals)
if ($case ==2){
#Starting Parameters VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV
$ClassInterval = list_random(0.001,0.002);
$MidLowest = list_random(0.05,0.06,0.07,0.08,0.09);
$MidLowest += $ClassInterval /2;  #band aid for cramped numbers on graph
$NumberClasses = list_random(4,5,6);

$n = random(int(2**($NumberClasses-1)),int(2**$NumberClasses-1), 1);
@probabilityPattern = ();
push  @probabilityPattern , 0..$NumberClasses-1;
push  @probabilityPattern , 1..$NumberClasses-2; #for a central preference

}  #end of case 2



#VVassigning values to classes VVVVVVVVVVVVVVVVVVVVVVVVVVVVV
$MAXfrequency = 0;
foreach $i (0.. $NumberClasses -1){$f[$i]=1}   # frequency at least 1 for each
foreach $i (0.. $n -1-$NumberClasses)   #one for each class already assigned


{

$tmpIndex = list_random(@probabilityPattern);
$f[$tmpIndex] += 1  ;
if ($f[$tmpIndex] > $MAXfrequency){$MAXfrequency = $f[$tmpIndex]}
}
#^^assigning values to classes ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

#VV finding the class(es) with the maximum frequency  VVVVVVVVVVVVVVVVVVV


@MaxClassMidpoint = (); #clearing history  - storing maximum clasc
@Rights = ();
@Lefts = ();


foreach $i (0.. $NumberClasses -1)
{
$Mids[$i]= $MidLowest + $ClassInterval * $i ;
$Lefts[$i]= $MidLowest + $ClassInterval * $i - $ClassInterval/2; 
$Rights[$i]= $MidLowest + $ClassInterval * $i + $ClassInterval/2; 
if ($f[$i] == $MAXfrequency){push @MaxClassMidpoint, $MidLowest + $ClassInterval * $i}  # max class midpoint
}


 $MAXfrequencyLISTOBJECT = List(@MaxClassMidpoint);

#^^  finding the class(es) with the maximum frequency  ^^^^^^^^^^^^^^^^^^^




#Starting Parameters ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#  Scaling horizantal positions VVVVVVVVVVVVV
$xAxisStart = max( $Lefts[0] - $ClassInterval ,0); #empty cell if not negative
$xWindowStart = $xAxisStart - $ClassInterval ;
$xAxisFinish = $Rights[$NumberClasses -1] + $ClassInterval ; #ditto
$xWindowFinish = $xAxisFinish ;
$xnumberGrids = ($xWindowFinish - $xWindowStart)/$ClassInterval ;
#  Scaling horizantal positions ^^^^^^^^^^^^^^^^

$yAxisStart = 0 ;
$yWindowStart = -1 ;
$yAxisFinish = $MAXfrequency + 1;
$yWindowFinish = $yAxisFinish ;
$ynumberGrids = $yWindowFinish - $yWindowStart ;





$graph = init_graph($xWindowStart,-1,$xWindowFinish,$yWindowFinish,
axes=>[$xAxisStart,0], grid=>[$xnumberGrids,$ynumberGrids],
size=>[400,400]); # or pixels=>[400,400]

$graph->lb('reset');

foreach my $i ($xAxisStart,$Lefts[0],@Rights){$graph->lb( new Label($i,0,$i,
    'black','center','top'))};

foreach my $i (0 .. $MAXfrequency){$graph->lb( new Label($xAxisStart,$i,$i,
    'black','right','bottom'))};


##junk








##graphing the bars vvvvvvvvvvvvvvvvvvvvvvv
$total = 0;
#$graph->new_color("randomcolor", random(160,240),random(160,240),random(160,240));
foreach $i (0.. $NumberClasses -1)

{

$graph->moveTo($Lefts[$i],0);


$graph->lineTo($Lefts[$i],$f[$i],'black',4);
$graph->lineTo($Rights[$i],$f[$i],'black',4);
$graph->lineTo($Rights[$i],0,'black',4);
$graph->lineTo($Lefts[$i],0);
$graph->new_color("randomcolor"."$i", random(160,240),random(160,240),random(160,240));

$graph->fillRegion([$Mids[$i],0.5,"randomcolor"."$i"]);
}

## graphing the bars ^^^^^^^^^^^^^^^^^^^^^


# questions  vvvvvvvvvvvvvvvvvvvv

# Greater than question VVVVVVVVVVVVVVVVv
$RandomPoint = random (1,$NumberClasses -3);  #ensuring two classes counted, one left out
$q4 = $Lefts[$RandomPoint];
$numberGreater = 0;
foreach $i ($RandomPoint .. $NumberClasses -1){$numberGreater +=$f[$i]}

# Greater than question  ^^^^^^^^^^^^^^^^^^


# Less than question VVVVVVVVVVVVVVVVv
$RandomPoint = random (1,$NumberClasses -2);  #ensuring two classes counted,one left out
$q5 = $Rights[$RandomPoint];
$numberLessThan = 0;
foreach $i (0 ..$RandomPoint ){$numberLessThan +=$f[$i]}

# Less than question  ^^^^^^^^^^^^^^^







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



#TEXT(beginproblem());
Context()->texStrings;

if ($case ==0){


#Labels on graphs VVVVVVVVVVVVVVVVVVV
$graph->lb( new Label(($xAxisStart+$xAxisFinish)/2,-0.5,'hourly salary (dollars)','black','center','top'));
$graph->lb( new Label($xAxisStart,$MAXfrequency +0.5,'number of employees','black','left','middle'));
#Labels on graphs ^^^^^^^^^^^^^^^^^^^^^

BEGIN_TEXT
$HR
A sample of the hourly wages of a number of employees at Coleman's Supermarkets is shown in the histogram below.
$BCENTER  $BR
\{ image( insertGraph($graph), 
width=>400,height=>400,tex_size=>800 ) \}
$ECENTER
$PAR
How many employees were surveyed?  \{ labeled_ans_rule("$trial"."n",15) \} 
$PAR
What is the Class Interval?  \{ labeled_ans_rule("$trial"."CI",15) \}
$PAR
The midpoint of the class with the highest frequency is  \{ labeled_ans_rule("$trial"."MP",15) \} $BR - separate by commas if there is more than one.


$PAR
How many employees earn  $DOLLAR \{sprintf("%.2f", $q4)\} or more \{ labeled_ans_rule("$trial"."MT",15) \}
$PAR 

$PAR
How many employees earn less than $DOLLAR \{sprintf("%.2f",$q5)\}\{labeled_ans_rule("$trial"."LT",15) \}
$PAR 
END_TEXT
}   # end case

if ($case ==1){


#Labels on graphs VVVVVVVVVVVVVVVVVVV
$graph->lb( new Label(($xAxisStart+$xAxisFinish)/2,-0.5,'Quiz Grade (%)','black','center','top'));
$graph->lb( new Label($xAxisStart,$MAXfrequency +0.5,'number of students','black','left','middle'));
#Labels on graphs ^^^^^^^^^^^^^^^^^^^^^

BEGIN_TEXT
$HR
The Professor gives his class a quiz.  $BR
The results are organized into the histogram shown below. $PAR
$BCENTER  $BR
\{ image( insertGraph($graph), 
width=>400,height=>400,tex_size=>800 ) \}
$ECENTER
$PAR
How many students are in the class?  \{ labeled_ans_rule("$trial"."n",15) \} 
$PAR
What is the Class Interval?  \{ labeled_ans_rule("$trial"."CI",15) \}
$PAR
The midpoint of the class with the highest frequency is  \{ labeled_ans_rule("$trial"."MP",15) \} $BR - separate by commas if there is more than one.


$PAR
How many students scored $q4  $PERCENT or more \{ labeled_ans_rule("$trial"."MT",15) \}
$PAR 

$PAR
How many students scored less than $q5 $PERCENT\{labeled_ans_rule("$trial"."LT",15) \}
$PAR 
END_TEXT
}   # end case


if ($case ==2){


#Labels on graphs VVVVVVVVVVVVVVVVVVV
$graph->lb( new Label(($xAxisStart+$xAxisFinish)/2,-0.5,'Active Intredient (grams)','black','center','top'));
$graph->lb( new Label($xAxisStart,$MAXfrequency +0.5,'number of pills','black','left','middle'));
#Labels on graphs ^^^^^^^^^^^^^^^^^^^^^

BEGIN_TEXT
$HR
A study is done to examine the amount of active ingredient in a certain pill  $BR
The results are organized into the histogram shown below. $PAR
$BCENTER  $BR
\{ image( insertGraph($graph), 
width=>400,height=>400,tex_size=>800 ) \}
$ECENTER
$PAR
How may pills were analyzed?  \{ labeled_ans_rule("$trial"."n",15) \} 
$PAR
What is the Class Interval?  \{ labeled_ans_rule("$trial"."CI",15) \}
$PAR
The midpoint of the class with the highest frequency is  \{ labeled_ans_rule("$trial"."MP",15) \} $BR - separate by commas if there is more than one.


$PAR
How many pills had $q4  grams or more \{ labeled_ans_rule("$trial"."MT",15) \}
$PAR 

$PAR
How many pills had less than $q5 grams\{labeled_ans_rule("$trial"."LT",15) \}
$PAR 
END_TEXT
}   # end case


#LABELED_ANS("numerical_answer" => num_cmp(12),"string_answer" => str_cmp("World") ); 
LABELED_ANS("$trial"."n"=> num_cmp($n) );
LABELED_ANS("$trial"."CI"=> num_cmp($ClassInterval) );
LABELED_ANS("$trial"."MP"=> $MAXfrequencyLISTOBJECT->cmp() );
LABELED_ANS("$trial"."MT"=> num_cmp($numberGreater) );
LABELED_ANS("$trial"."LT"=> num_cmp($numberLessThan) );
}




ENDDOCUMENT();