.variance-calculator-wrapper {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
max-width: 800px;
margin: 20px auto;
padding: 25px;
background: #f9f9f9;
border-radius: 10px;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.1);
border: 1px solid #e0e0e0;
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text-align: center;
color: #333;
margin-bottom: 20px;
font-size: 2em;
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.variance-calculator-wrapper p {
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line-height: 1.6;
color: #555;
}
.calculator-input-group {
margin-bottom: 20px;
}
.calculator-input-group label {
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margin-bottom: 8px;
font-weight: bold;
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.calculator-input-group textarea {
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box-sizing: border-box;
resize: vertical;
min-height: 100px;
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.calculator-input-group input[type="radio"] {
margin-right: 8px;
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}
.calculator-input-group label[for="populationVariance"],
.calculator-input-group label[for="sampleVariance"] {
display: inline-block;
font-weight: normal;
margin-right: 20px;
color: #555;
}
.variance-calculator-wrapper button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 5px;
font-size: 1.1em;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 20px;
}
.variance-calculator-wrapper button:hover {
background-color: #0056b3;
}
.calculator-result {
margin-top: 25px;
padding: 15px;
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border: 1px solid #d4edda;
border-radius: 8px;
color: #155724;
font-size: 1.05em;
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.calculator-result h3 {
color: #007bff;
margin-top: 0;
margin-bottom: 10px;
font-size: 1.4em;
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.calculator-result p {
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.calculator-result strong {
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function calculateVariance() {
var dataInput = document.getElementById("dataPoints").value;
var numbers = dataInput.split(/[\s,]+/).filter(function(n) {
return !isNaN(parseFloat(n)) && n.trim() !== ";
}).map(Number);
var resultDiv = document.getElementById("varianceResult");
resultDiv.innerHTML = ""; // Clear previous results
if (numbers.length === 0) {
resultDiv.innerHTML = "Please enter at least one valid number.";
return;
}
// Calculate Mean
var sum = 0;
for (var i = 0; i < numbers.length; i++) {
sum += numbers[i];
}
var mean = sum / numbers.length;
// Calculate Sum of Squared Differences
var sumOfSquaredDifferences = 0;
for (var i = 0; i < numbers.length; i++) {
sumOfSquaredDifferences += Math.pow(numbers[i] – mean, 2);
}
var variance = 0;
var standardDeviation = 0;
var varianceType = document.querySelector('input[name="varianceType"]:checked').value;
if (varianceType === "population") {
variance = sumOfSquaredDifferences / numbers.length;
standardDeviation = Math.sqrt(variance);
resultDiv.innerHTML += "Variance Calculator
Understanding the spread of data is crucial in statistics, and variance is a fundamental measure that quantifies this spread. This calculator helps you determine both population and sample variance for a given set of data points.
What is Variance?
Variance is a statistical measurement that assesses the spread between numbers in a data set. More specifically, it measures how far each number in the set is from the mean (average) and, therefore, from every other number in the set. A high variance indicates that data points are very spread out from the mean and from each other, while a low variance indicates that data points are clustered closely around the mean.
Why is Variance Important?
- Data Distribution: It provides insight into the distribution of data, helping to understand its consistency or variability.
- Risk Assessment: In finance, variance is used to measure the volatility of an investment. Higher variance often implies higher risk.
- Quality Control: In manufacturing, low variance in product measurements indicates high quality and consistency.
- Foundation for Other Statistics: Variance is a key component in calculating other important statistical measures, such as standard deviation, which is simply the square root of the variance.
Population Variance vs. Sample Variance
There are two main types of variance, depending on whether you have data for an entire population or just a sample of that population:
- Population Variance (σ²): This is used when you have data for every member of an entire group (the population). The formula involves dividing the sum of squared differences from the mean by the total number of data points (N).
- Sample Variance (s²): This is used when you only have data for a subset (a sample) of a larger population. Because a sample tends to underestimate the true population variance, the formula uses a slightly different denominator: the sum of squared differences from the mean is divided by (n – 1), where 'n' is the number of data points in the sample. This adjustment, known as Bessel's correction, provides a more accurate estimate of the population variance from a sample.
How to Use the Calculator
Simply enter your numerical data points into the text area, separated by commas or newlines. Then, select whether you want to calculate the "Population Variance" or "Sample Variance" and click "Calculate Variance." The calculator will provide the variance and the corresponding standard deviation.
Variance Calculation Tool
Enter your data points below, separated by commas or newlines. Then select the type of variance you wish to calculate.
Example Calculation
Let's consider a simple data set: 2, 4, 4, 4, 5, 5, 7, 9
- Calculate the Mean (Average):
(2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) / 8 = 40 / 8 = 5 - Calculate the Squared Difference from the Mean for Each Data Point:
- (2 – 5)² = (-3)² = 9
- (4 – 5)² = (-1)² = 1
- (4 – 5)² = (-1)² = 1
- (4 – 5)² = (-1)² = 1
- (5 – 5)² = (0)² = 0
- (5 – 5)² = (0)² = 0
- (7 – 5)² = (2)² = 4
- (9 – 5)² = (4)² = 16
- Sum of Squared Differences:
9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32 - Calculate Variance:
- Population Variance (N=8): 32 / 8 = 4
- Sample Variance (n-1=7): 32 / 7 ≈ 4.5714
- Calculate Standard Deviation:
- Population Standard Deviation: √4 = 2
- Sample Standard Deviation: √4.5714 ≈ 2.1381
This example demonstrates how the calculator processes your input to arrive at these key statistical measures.