This calculator helps you apply a bell curve to student scores, adjusting them based on the distribution of the class. A bell curve, also known as a normal distribution, is a statistical model that approximates many real-world phenomena. In grading, it's used to adjust raw scores so that the class average falls around a desired point (often a C or B), with scores spreading out normally around that average.
function calculateBellCurveGrade() {
var rawScore = parseFloat(document.getElementById("rawScore").value);
var classAverage = parseFloat(document.getElementById("classAverage").value);
var desiredAverage = parseFloat(document.getElementById("desiredAverage").value);
var standardDeviation = parseFloat(document.getElementById("standardDeviation").value);
var maxScore = parseFloat(document.getElementById("maxScore").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
// Input validation
if (isNaN(rawScore) || isNaN(classAverage) || isNaN(desiredAverage) || isNaN(standardDeviation) || isNaN(maxScore)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (standardDeviation <= 0) {
resultDiv.innerHTML = "Standard deviation must be a positive number.";
return;
}
if (rawScore < 0 || classAverage < 0 || desiredAverage < 0 || maxScore maxScore) {
resultDiv.innerHTML = "Scores and maximum score must be non-negative, and raw score cannot exceed maximum score.";
return;
}
// Bell curve calculation formula
// The core idea is to shift and scale the scores.
// First, calculate the difference between the student's score and the class average.
// Then, scale this difference by the ratio of the desired average to the current average (or a factor related to standard deviation).
// A common approach is to normalize the score relative to the class average and standard deviation,
// and then rescale it to the desired average.
// Let's use a common additive and multiplicative adjustment:
// New Score = Desired Average + (Student's Score – Class Average) * (Desired Average / Class Average)
// However, this can lead to issues if class average is 0 or if scaling is too aggressive.
// A more robust method often involves standard scores (z-scores) and then mapping them.
// z_score = (rawScore – classAverage) / standardDeviation
// new_rawScore = desiredAverage + z_score * standardDeviation
// This is essentially an additive shift if standard deviation remains the same.
// A more common bell curve grading involves adjusting based on the difference between the desired average and the current average,
// distributed across the standard deviation.
// Method 1: Simple Additive/Multiplicative Adjustment (can be problematic)
// var scoreDifference = rawScore – classAverage;
// var scalingFactor = desiredAverage / classAverage; // Problem if classAverage is 0
// var adjustedScore = classAverage + scoreDifference * scalingFactor;
// Method 2: Using Z-scores and re-mapping (more robust)
var zScore = (rawScore – classAverage) / standardDeviation;
var adjustedScore = desiredAverage + (zScore * standardDeviation);
// Ensure the adjusted score doesn't exceed the maximum possible score or go below 0.
adjustedScore = Math.min(adjustedScore, maxScore);
adjustedScore = Math.max(adjustedScore, 0);
// Round to a reasonable number of decimal places for a grade
adjustedScore = parseFloat(adjustedScore.toFixed(2));
resultDiv.innerHTML = "Original Score: " + rawScore + "" +
"Class Average (Raw): " + classAverage + "" +
"Desired Average: " + desiredAverage + "" +
"Standard Deviation: " + standardDeviation + "" +
"Bell Curved Grade: " + adjustedScore + "";
}
.bell-curve-calculator {
font-family: sans-serif;
border: 1px solid #ccc;
padding: 20px;
border-radius: 8px;
max-width: 500px;
margin: 20px auto;
background-color: #f9f9f9;
}
.bell-curve-calculator h2 {
text-align: center;
color: #333;
margin-bottom: 15px;
}
.bell-curve-calculator p {
line-height: 1.6;
color: #555;
margin-bottom: 15px;
}
.inputs {
margin-bottom: 20px;
}
.input-group {
margin-bottom: 15px;
}
.input-group label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #444;
}
.input-group input {
width: calc(100% – 20px);
padding: 10px;
border: 1px solid #ddd;
border-radius: 4px;
box-sizing: border-box; /* Include padding and border in the element's total width and height */
}
.bell-curve-calculator button {
display: block;
width: 100%;
padding: 12px 15px;
background-color: #007bff;
color: white;
border: none;
border-radius: 5px;
font-size: 16px;
cursor: pointer;
transition: background-color 0.3s ease;
}
.bell-curve-calculator button:hover {
background-color: #0056b3;
}
#result {
margin-top: 25px;
padding: 15px;
border: 1px dashed #ccc;
background-color: #fff;
border-radius: 5px;
text-align: center;
}
#result p {
margin: 5px 0;
color: #333;
}
#result strong {
color: #d9534f; /* A distinct color for the final result */
}