在php中使用加权平均值评分答案

【问题标题】：Grading using weighted averages in php在php中使用加权平均值评分
【发布时间】：2016-07-11 14:57:20
【问题描述】：

我如何用 php 给这个测试评分？我需要一个百分比分数...

我有一系列问题，其中包含正确/不正确的布尔值和相应的权重。

我需要先找到正确答案的平均值吗？

等式是什么？

$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'];
    }
}

【问题讨论】：

标签： php weighted-average

【解决方案1】：

您可以计算候选人获得的权重（即您拥有的分数），然后计算可能的总权重（即满分）。

然后你可以将候选分数除以总分：

分数 = 候选人分数 / 总分

从那里你可以计算百分比：

百分比 = 分数 * 100

使用您的代码：

$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;

【讨论】：

【解决方案2】：

通常情况下，平均值（加权或不加权）是所有可能事物的总和。如果它是加权的，这通常意味着每个事物不是 1 事物，而是实际上是 weightOfThing 事物。

例子：

$totalQuestions = count($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;

【讨论】：

【解决方案3】：

可以优化，但这里是完整的方程式：

$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);

【讨论】：