Please enter a valid data set with at least two numbers.
Calculation Results
Count (N):0
Mean (μ or x̄):0
Sum of Squares:0
Variance (s² or σ²):0
Standard Deviation:0
Understanding Standard Deviation
Standard deviation is a crucial statistical measure that quantifies the amount of variation or dispersion in a set of values. A low standard deviation indicates that the data points tend to be close to the mean (average) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.
Sample vs. Population: Which One to Choose?
When using a standard deviation calculator, you must decide between the "Sample" and "Population" methods. This choice depends on the source of your data:
Population Standard Deviation (σ): Used when your data set represents the entire group you are interested in (e.g., the heights of all students in a specific classroom).
Sample Standard Deviation (s): Used when your data is a subset or "sample" of a larger population (e.g., surveying 100 people to estimate the behavior of an entire city). It uses Bessel's correction (n-1) to provide an unbiased estimate.
How is it Calculated?
The process follows these mathematical steps:
Find the arithmetic mean (average) of the data set.
Subtract the mean from each individual data point and square the result.
Calculate the sum of all those squared values.
Divide the sum by the number of data points (N) for population, or (N-1) for sample. This result is the Variance.
Take the square root of the variance to find the Standard Deviation.
Practical Example
Imagine you are measuring the weight of 5 apples in grams: 150, 155, 145, 160, 150.
Metric
Result (Sample)
Count (N)
5
Mean
152
Variance
32.5
Standard Deviation
5.70
In this example, a standard deviation of 5.70 tells us that most apples in this batch weigh within roughly 5.7 grams of the 152g average.
function calculateStandardDeviation() {
var rawInput = document.getElementById('dataSet').value;
var errorDiv = document.getElementById('errorMsg');
var resultsDiv = document.getElementById('results');
// Split by commas, spaces, or newlines and clean up
var numbers = rawInput.split(/[,\s\n]+/)
.filter(function(item) { return item !== "" && !isNaN(parseFloat(item)); })
.map(Number);
if (numbers.length < 2) {
errorDiv.style.display = 'block';
resultsDiv.style.display = 'none';
return;
}
errorDiv.style.display = 'none';
var n = numbers.length;
var isSample = document.getElementById('typeSample').checked;
// 1. Calculate Mean
var sum = 0;
for (var i = 0; i < n; i++) {
sum += numbers[i];
}
var mean = sum / n;
// 2. Sum of Squares
var sumSq = 0;
for (var j = 0; j < n; j++) {
sumSq += Math.pow(numbers[j] – mean, 2);
}
// 3. Variance
var divisor = isSample ? (n – 1) : n;
var variance = sumSq / divisor;
// 4. Standard Deviation
var stdDev = Math.sqrt(variance);
// Display results
document.getElementById('resCount').innerText = n;
document.getElementById('resMean').innerText = mean.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4});
document.getElementById('resSumSq').innerText = sumSq.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4});
document.getElementById('resVariance').innerText = variance.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4});
document.getElementById('resSD').innerText = stdDev.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4});
resultsDiv.style.display = 'block';
}