Grading using weighted averages in php

Question

How could I grade this test with php? I need a percentage score...

I have an array of questions containing the correct / incorrect bool and the corresponding weight.

Do I need to find the average of correct answers first?

What would the equation be?

$questions = array(
    0=>array(
        'Question'=>"Some Question",
        'Correct'=>true,
        'Weight'=>5,
    ),
    1=>array(
        'Question'=>"Some Question",
        'Correct'=>false,
        'Weight'=>5,
    ),
    2=>array(
        'Question'=>"Some Question",
        'Correct'=>true,
        'Weight'=>4,
    ),
    3=>array(
        'Question'=>"Some Question",
        'Correct'=>true,
        'Weight'=>0,
    ),
    4=>array(
        'Question'=>"Some Question",
        'Correct'=>false,
        'Weight'=>5,
    ),
    5=>array(
        'Question'=>"Some Question",
        'Correct'=>true,
        'Weight'=>4,
    ),
);
$weights = array(
    0=>0
    1=>0
    2=>.05
    3=>.20
    4=>.25
    5=>.50
);
$totalQuestions=0;
$correctAnswers=0;
$points=0;
foreach($questions as $question){
    $totalQuestions++;
    if($question['Correct']){
        $correctAnswers++;
        $points = $points = $weights[$question['Weight'];
    }
}

score 0 · Answer 1 · answered Jul 11 '16 at 15:07

Typically an average (weighted or not) is the sum of things over the total possible things. If it's weighted that usually means that each thing is not 1 thing but in reality is weightOfThing things.

Example:

$totalQuestions = count($questions); //No need to increment
$totalWeight = 0; //Could do a sum here but no need
$weightedSum = 0;
foreach($questions as $question){
    $totalWeight += isset($question["Weight"])?$question["Weight"]:0; //Assume a question with no weight has 0 weight, i.e., doesn't count. Adjust accordingly
    if($question['Correct']){
        $weightedSum += isset($question["Weight"])?$question["Weight"]:0;
    }
}
$weightedAverage = $weightedSum / $totalWeight;

score 0 · Accepted Answer · answered Jul 11 '16 at 15:16

You can calculate the amount of weights the candidate earned (i.e. the points you have) and then the total weights possible (i.e. a perfect score).

Then you can divide the candidate score by the total score:

Score = Candidate score / Total Score

From there you can calculate the percentage:

Percentage = Score * 100

Using your code:

$totalQuestions=0;
$totalWeights=0;
$correctAnswers=0;
$weightsEarned=0;
foreach($questions as $question){
    $totalQuestions++;
    $totalWeights+=$weights[$question['Weight']];
    if($question['Correct']){
        $correctAnswers++;
        $weightsEarned += $weights[$question['Weight']];
    }
}

echo "Score Overview: ";
echo "<br/>Weights Earned: " . $weightsEarned;
echo "<br/>Correct Answers: " . $correctAnswers;
echo "<br/>Total Weights Possible : " . $totalWeights;
echo "<br/>Percentage Earned: " . ($weightsEarned / $totalWeights) * 100;

score 0 · Answer 3 · answered Jul 13 '16 at 18:00

could be optimized but here is the completed equation:

$weights = array(
    0=>0,
    1=>0,
    2=>.05,
    3=>.20,
    4=>.25,
    5=>.50,
);

$byWeight = array();
foreach($questions as $question){
    //$totalQuestions++;
    $byWeight[$question['Weight']]['TotalNumberOfQuestionsForWeight']++;
    if($question['Correct']){
        $byWeight[$question['Weight']]['CorrectAnswers']++;
    }
}

$totalWeightsSum = 0;
foreach($byWeight as $weight => $data){
     $totalWeightsSum = $totalWeightsSum + (($data['CorrectAnswers'] / $data['TotalNumberOfQuestionsForWeight']) * $weights[$weight]);
}

echo '<pre>'.var_export($byWeight,1).'</pre>';
echo $totalWeightsSum / array_sum($weights);

Grading using weighted averages in php

3 Answers3