Instantly compute the weighted average variance for financial portfolios, statistical pooling, or quality control datasets.
Weighted Average Variance Calculator
Enter your data sets below. Weights can be probabilities, sample sizes, or portfolio percentages.
E.g., Sample size or % allocation
Please enter a positive number
The variance of this specific set
Variance cannot be negative
Weighted Average Variance
0.00
Formula applied: Σ (Weight × Variance) / Σ Weights
Total Weight
0
Weighted Std Dev
0.00
Number of Sets
0
Figure 1: Comparison of individual set variances against the calculated weighted average variance.
Detailed Breakdown of Variance Contribution
Set #
Weight (w)
Variance (σ²)
Product (w × σ²)
Impact %
What is Calculate Weighted Average Variance?
When you need to calculate weighted average variance, you are performing a statistical operation that determines the average variability across multiple datasets, adjusting for the size or importance (weight) of each specific dataset. Unlike a simple arithmetic mean, which treats all inputs equally, a weighted average ensures that larger samples or more heavily weighted assets have a proportional influence on the final result.
This calculation is critical in fields ranging from financial portfolio management—where it helps assess the risk of combined asset classes—to manufacturing quality control, where pooled variance is used to understand system consistency across different production batches.
Common misconceptions include confusing this with "variance of the weighted mean" (which involves squaring weights and is used for standard error) or assuming that weights must always equal 100% (or 1.0). While percentages are common, raw sample sizes can also serve as valid weights.
Weighted Average Variance Formula and Mathematical Explanation
To accurately calculate weighted average variance, we use a formula that sums the product of each item's weight and its variance, then divides by the total sum of the weights. This is mathematically expressed as:
An investor holds two funds. Fund A represents 70% of the portfolio with a variance of 15. Fund B represents 30% with a variance of 40. To understand the average volatility exposure of the holdings (ignoring correlation for this specific metric):
Fund A: 0.70 × 15 = 10.5
Fund B: 0.30 × 40 = 12.0
Sum of Products: 22.5
Sum of Weights: 1.0
Weighted Average Variance: 22.5
This figure helps the investor realize that despite Fund B being small, its high variance contributes significantly to the average instability.
Example 2: Manufacturing Tolerances
A factory produces screws on two machines. Machine 1 produces 1,000 units with a variance of 0.02 mm². Machine 2 produces 500 units with a variance of 0.05 mm².
Machine 1: 1000 × 0.02 = 20
Machine 2: 500 × 0.05 = 25
Total Weight: 1,500
Calculation: (20 + 25) / 1500 = 0.03 mm²
The pooled variance indicates the overall consistency of the batch sent to the client.
How to Use This Calculator
Identify your datasets: Determine how many distinct groups, assets, or samples you have.
Input Weight: Enter the size, percentage, or importance factor for each set. Ensure these are non-negative.
Input Variance: Enter the statistical variance (σ²) for each set. If you only have Standard Deviation, square it first.
Review Results: The tool instantly updates to show the weighted average. Use the chart to visually identify outliers.
Analyze the Table: Check the "Impact %" column to see which specific set is driving the weighted average up or down.
Key Factors That Affect Results
When you calculate weighted average variance, several factors influence the final metric:
Sample Size Disparity: A very large weight on a low-variance item will pull the average down aggressively, masking volatility in smaller subsets.
Outlier Variances: A single asset with extreme variance can skew the result, even if its weight is moderate.
Data Accuracy: Variance is squared deviation; small errors in measuring the base data are magnified when squared.
Correlation (Contextual): While this calculator computes the weighted mean of variances, in portfolio theory, correlation between assets affects the portfolio variance differently than the weighted average of variances.
Time Horizon: In finance, variance changes over time. Annualized variance will differ significantly from daily variance.
Measurement Units: Ensure all variances are in the same unit scale before calculation.
Frequently Asked Questions (FAQ)
Can weights be negative?
No. In standard statistics and finance, weights (sample sizes or probabilities) cannot be negative. Negative weights would render the weighted average variance meaningless.
Is Weighted Average Variance the same as Pooled Variance?
Yes, in the context of combining samples with different sizes, the calculation mirrors the formula for pooled variance, assuming the means are separate or irrelevant to the variance aggregation.
Do weights need to add up to 100?
No. The calculator automatically divides by the sum of the weights. You can use raw counts (e.g., 500, 200, 300) or decimals (0.5, 0.2, 0.3).
How do I convert Standard Deviation to Variance?
Simply multiply the standard deviation by itself. For example, if σ = 5, then Variance (σ²) = 25.
Why is my result NaN?
This usually happens if you enter text instead of numbers, or if the sum of weights is zero. Ensure at least one weight is greater than zero.
Can I use this for stock portfolios?
You can use it to find the average variance of the components, but to find the total risk of the portfolio (Portfolio Variance), you must also account for covariance/correlation between stocks.
What is a good weighted average variance?
There is no universal "good" number; it depends on the context. In manufacturing, lower is better (higher consistency). In finance, higher variance implies higher risk (but potentially higher reward).
Does this calculator handle empty rows?
Yes. The algorithm ignores rows where Weight or Variance is missing or zero, ensuring they don't corrupt the calculation.
Related Tools and Internal Resources
Explore more of our statistical and financial tools to enhance your analysis:
// Main Calculation Logic
function calculate() {
var totalWeight = 0;
var weightedSum = 0;
var items = [];
var result = 0;
// Loop through 5 possible inputs
for (var i = 1; i <= 5; i++) {
var wInput = document.getElementById('weight' + i);
var vInput = document.getElementById('var' + i);
// Basic validation
if (!wInput || !vInput) continue;
var wVal = parseFloat(wInput.value);
var vVal = parseFloat(vInput.value);
// Reset error states
var errW = document.getElementById('err-weight' + i);
var errV = document.getElementById('err-var' + i);
if (errW) errW.style.display = 'none';
if (errV) errV.style.display = 'none';
// Check if inputs are numbers
if (!isNaN(wVal) && !isNaN(vVal)) {
// Logic Validation
if (wVal < 0) {
if (errW) errW.style.display = 'block';
continue;
}
if (vVal 0) {
totalWeight += wVal;
weightedSum += (wVal * vVal);
items.push({
id: i,
w: wVal,
v: vVal,
product: wVal * vVal
});
}
}
}
// Calculate Result
if (totalWeight > 0) {
result = weightedSum / totalWeight;
} else {
result = 0;
}
// Update DOM
document.getElementById('result').innerText = formatNumber(result, 4);
document.getElementById('totalWeight').innerText = formatNumber(totalWeight, 2);
document.getElementById('weightedStdDev').innerText = formatNumber(Math.sqrt(result), 4);
document.getElementById('countSets').innerText = items.length;
updateTable(items, totalWeight);
updateChart(items, result);
}
// Helper: Format Number
function formatNumber(num, decimals) {
return num.toLocaleString(undefined, {
minimumFractionDigits: decimals,
maximumFractionDigits: decimals
});
}
// Update Table Function
function updateTable(items, totalW) {
var tbody = document.getElementById('breakdownTableBody');
tbody.innerHTML = ";
if (items.length === 0) {
tbody.innerHTML = '
No valid data entered
';
return;
}
var totalProduct = 0;
// Calculate total product first for impact % if needed (though impact on avg is simpler)
// Impact % here defined as contribution to the weighted sum relative to total weighted sum
// OR relative to the final Average. Let's do contribution to weighted sum.
for(var k=0; k<items.length; k++) {
totalProduct += items[k].product;
}
for (var i = 0; i 0) {
impact = (item.product / totalProduct) * 100;
}
tr.innerHTML =
'
Set ' + item.id + '
' +
'
' + formatNumber(item.w, 2) + '
' +
'
' + formatNumber(item.v, 4) + '
' +
'
' + formatNumber(item.product, 2) + '
' +
'
' + formatNumber(impact, 1) + '%
';
tbody.appendChild(tr);
}
}
// Update Chart Function (Canvas)
function updateChart(items, avg) {
var canvas = document.getElementById('varianceChart');
var ctx = canvas.getContext('2d');
var width = canvas.width = canvas.offsetWidth;
var height = canvas.height = canvas.offsetHeight;
// Clear
ctx.clearRect(0, 0, width, height);
if (items.length === 0) return;
// Dimensions
var padding = 40;
var chartWidth = width – (padding * 2);
var chartHeight = height – (padding * 2);
// Find max value for scaling (Items + Average)
var maxVal = avg;
for (var i = 0; i maxVal) maxVal = items[i].v;
}
maxVal = maxVal * 1.2; // Add headroom
if (maxVal === 0) maxVal = 1;
var barWidth = chartWidth / (items.length + 1) / 2;
var spacing = chartWidth / (items.length + 1);
// Draw Axes
ctx.beginPath();
ctx.moveTo(padding, padding);
ctx.lineTo(padding, height – padding);
ctx.lineTo(width – padding, height – padding);
ctx.strokeStyle = '#dee2e6';
ctx.stroke();
// Draw Bars
for (var i = 0; i < items.length; i++) {
var x = padding + (spacing * (i + 0.5));
var barH = (items[i].v / maxVal) * chartHeight;
var y = height – padding – barH;
// Bar
ctx.fillStyle = '#004a99';
ctx.fillRect(x, y, barWidth, barH);
// Label
ctx.fillStyle = '#212529';
ctx.font = '12px Arial';
ctx.textAlign = 'center';
ctx.fillText('Set ' + items[i].id, x + (barWidth/2), height – padding + 15);
ctx.fillText(items[i].v.toFixed(1), x + (barWidth/2), y – 5);
}
// Draw Average Bar (Last)
var avgX = padding + (spacing * (items.length + 0.5));
var avgH = (avg / maxVal) * chartHeight;
var avgY = height – padding – avgH;
ctx.fillStyle = '#28a745';
ctx.fillRect(avgX, avgY, barWidth, avgH);
ctx.fillStyle = '#212529';
ctx.fillText('AVG', avgX + (barWidth/2), height – padding + 15);
ctx.font = 'bold 12px Arial';
ctx.fillText(avg.toFixed(1), avgX + (barWidth/2), avgY – 5);
// Legend
ctx.fillStyle = '#004a99';
ctx.fillRect(width – 120, 10, 10, 10);
ctx.fillStyle = '#6c757d';
ctx.textAlign = 'left';
ctx.fillText('Set Variance', width – 105, 19);
ctx.fillStyle = '#28a745';
ctx.fillRect(width – 120, 30, 10, 10);
ctx.fillStyle = '#6c757d';
ctx.fillText('Weighted Avg', width – 105, 39);
}
// Reset
function resetCalculator() {
document.getElementById('weight1').value = "10";
document.getElementById('var1').value = "5.5";
document.getElementById('weight2').value = "15";
document.getElementById('var2').value = "8.2";
document.getElementById('weight3').value = "25";
document.getElementById('var3').value = "4.1";
document.getElementById('weight4').value = "";
document.getElementById('var4').value = "";
document.getElementById('weight5').value = "";
document.getElementById('var5').value = "";
calculate();
}
// Copy Results
function copyResults() {
var res = document.getElementById('result').innerText;
var std = document.getElementById('weightedStdDev').innerText;
var txt = "Calculated Weighted Average Variance: " + res + "\n";
txt += "Weighted Standard Deviation: " + std + "\n";
txt += "Generated by FinancialCalc Tools";
var temp = document.createElement('textarea');
temp.value = txt;
document.body.appendChild(temp);
temp.select();
document.execCommand('copy');
document.body.removeChild(temp);
var btn = document.querySelector('.btn-copy');
var originalText = btn.innerText;
btn.innerText = "Copied!";
setTimeout(function(){ btn.innerText = originalText; }, 2000);
}
// Init
window.onload = function() {
calculate();
// Window resize listener for canvas redraw
window.addEventListener('resize', function() {
calculate();
});
};