function calculateVariance() {
var rawInput = document.getElementById('dataInput').value;
var errorArea = document.getElementById('errorArea');
var resultsArea = document.getElementById('resultsArea');
errorArea.style.display = 'none';
resultsArea.style.display = 'none';
// Clean input: replace commas with spaces, split by whitespace, convert to numbers
var cleanInput = rawInput.replace(/,/g, ' ').trim();
if (!cleanInput) {
errorArea.innerHTML = "Please enter some numbers to calculate.";
errorArea.style.display = 'block';
return;
}
var strArray = cleanInput.split(/\s+/);
var numArray = [];
for (var i = 0; i < strArray.length; i++) {
var num = parseFloat(strArray[i]);
if (!isNaN(num)) {
numArray.push(num);
}
}
var n = numArray.length;
if (n < 2) {
errorArea.innerHTML = "Variance requires at least two data points.";
errorArea.style.display = 'block';
return;
}
var isSample = document.querySelector('input[name="varianceType"]:checked').value === 'sample';
// Step 1: Sum and Mean
var sum = 0;
for (var j = 0; j < n; j++) {
sum += numArray[j];
}
var mean = sum / n;
// Step 2: Sum of Squares
var sumOfSquares = 0;
for (var k = 0; k < n; k++) {
sumOfSquares += Math.pow(numArray[k] – mean, 2);
}
// Step 3: Variance
var divisor = isSample ? (n – 1) : n;
var variance = sumOfSquares / divisor;
var stdDev = Math.sqrt(variance);
// Display Results
document.getElementById('resCount').innerText = n;
document.getElementById('resSum').innerText = sum.toFixed(4).replace(/\.?0+$/, "");
document.getElementById('resMean').innerText = mean.toFixed(4).replace(/\.?0+$/, "");
document.getElementById('resVariance').innerText = variance.toFixed(6).replace(/\.?0+$/, "");
document.getElementById('resStdDev').innerText = stdDev.toFixed(6).replace(/\.?0+$/, "");
document.getElementById('resSS').innerText = sumOfSquares.toFixed(4).replace(/\.?0+$/, "");
resultsArea.style.display = 'block';
}
Understanding Statistical Variance
Variance is a fundamental statistical measurement used to describe the spread or dispersion of data points in a set. In simpler terms, it measures how far each number in the set is from the mean (average) and thus from every other number in the set.
Sample vs. Population Variance
Choosing the correct data type is crucial for accurate statistical analysis:
Population Variance: Used when your dataset represents the entire group you are interested in (e.g., the test scores of every student in a specific classroom).
Sample Variance: Used when your dataset is a subset of a larger population (e.g., surveying 100 random people to estimate the behavior of a whole country). It uses Bessel's correction (n-1) to provide an unbiased estimate.
How to Calculate Variance Manually
Find the Mean: Add all numbers and divide by the total count (n).
Subtract the Mean: For every individual number, subtract the mean and square the result (this ensures the result is positive).
Sum of Squares: Add all those squared results together.
Divide: For population variance, divide by n. For sample variance, divide by n – 1.
Practical Example
Imagine you are measuring the height of 5 plants in centimeters: 10, 12, 14, 16, and 18.
Variance is used extensively in finance to measure volatility and risk, in manufacturing to ensure quality control consistency, and in science to determine the reliability of experimental results. While standard deviation is often preferred for reporting because it is in the same units as the original data, variance is the mathematical engine that drives these deeper insights.