Standard Deviation and Variance Calculator
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Standard Deviation & Variance Calculator
Results
Variance: –
Standard Deviation: –
Variance: – | Standard Deviation: –
Understanding Standard Deviation and Variance
In statistics, variance and standard deviation are two fundamental measures of data dispersion or spread. They quantify how much the individual data points in a dataset deviate from the mean (average) of that dataset. A low variance or standard deviation indicates that the data points tend to be close to the mean, while a high value suggests that the data points are spread out over a wider range.
What is Variance?
Variance measures the average of the squared differences from the mean. It is calculated by taking the difference between each data point and the mean, squaring that difference, summing up all these squared differences, and then dividing by the number of data points (for population variance) or by the number of data points minus one (for sample variance). This calculator computes the sample variance, which is generally used when your data is a sample from a larger population.
The formula for sample variance (s²) is:
s² = Σ(xi - x̄)² / (n - 1)
Where:
s² is the sample varianceΣ is the summation symbol (sum of)xi is each individual data pointx̄ is the sample mean (average)n is the number of data points
What is Standard Deviation?
Standard deviation is simply the square root of the variance. It is a more intuitive measure of spread because it is expressed in the same units as the original data. A standard deviation of 0 means all values are identical.
The formula for sample standard deviation (s) is:
s = √[ Σ(xi - x̄)² / (n - 1) ]
This means the standard deviation is the square root of the variance.
How to Use This Calculator
- Enter your numerical data points into the "Data Points" field. Separate each number with a comma.
- Click the "Calculate" button.
- The calculator will display the computed sample variance and sample standard deviation for your dataset.
Use Cases
Variance and standard deviation are crucial in various fields:
- Finance: Measuring the volatility of an investment or the risk associated with a portfolio.
- Quality Control: Monitoring the consistency of manufactured products.
- Science and Research: Analyzing experimental data and understanding the reliability of results.
- Social Sciences: Examining the distribution of survey responses or demographic data.
- Education: Understanding the spread of student scores on tests.
function calculateStats() {
var dataInput = document.getElementById("dataPoints").value;
var dataPointsArray = dataInput.split(',');
var numbers = [];
for (var i = 0; i < dataPointsArray.length; i++) {
var trimmedValue = dataPointsArray[i].trim();
if (trimmedValue !== "") {
var num = parseFloat(trimmedValue);
if (!isNaN(num)) {
numbers.push(num);
}
}
}
if (numbers.length < 2) {
document.getElementById("varianceResult").textContent = "N/A";
document.getElementById("stdDevResult").textContent = "N/A";
document.getElementById("varianceValue").textContent = "N/A";
document.getElementById("stdDevValue").textContent = "N/A";
alert("Please enter at least two valid numbers to calculate variance and standard deviation.");
return;
}
var n = numbers.length;
var sum = 0;
for (var i = 0; i < n; i++) {
sum += numbers[i];
}
var mean = sum / n;
var sumOfSquaredDifferences = 0;
for (var i = 0; i < n; i++) {
sumOfSquaredDifferences += Math.pow(numbers[i] – mean, 2);
}
// Calculate Sample Variance (n-1 denominator)
var variance = sumOfSquaredDifferences / (n – 1);
// Calculate Sample Standard Deviation
var stdDev = Math.sqrt(variance);
document.getElementById("varianceResult").textContent = variance.toFixed(4);
document.getElementById("stdDevResult").textContent = stdDev.toFixed(4);
document.getElementById("varianceValue").textContent = variance.toFixed(4);
document.getElementById("stdDevValue").textContent = stdDev.toFixed(4);
}