Calculate the variance, mean, and deviation for your data set.
Count (N):0
Mean (Average):0
Variance:0
Standard Deviation:0
How to Calculate Standard Deviation
Standard deviation is a statistical tool used to determine the amount of variation or dispersion in a set of data values. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values.
The Step-by-Step Process
Find the Mean: Add all numbers together and divide by the total count.
Subtract the Mean: For each number in your set, subtract the mean and square the result. This ensures all values are positive.
Calculate Variance: Find the average of those squared differences.
For Population Variance, divide by N (the total number of items).
For Sample Variance, divide by N-1 (useful when calculating a small subset of a larger group).
Square Root: Take the square root of the variance to get the Standard Deviation.
Standard Deviation (σ) = √[ Σ(x – μ)² / N ]
Example Calculation
Let's say you have a data set of test scores: 10, 20, 30.
Mean: (10 + 20 + 30) / 3 = 20
Squared Deviations:
(10 – 20)² = 100
(20 – 20)² = 0
(30 – 20)² = 100
Sum of Squares: 100 + 0 + 100 = 200
Sample Variance (N-1): 200 / 2 = 100
Standard Deviation: √100 = 10
Sample vs. Population: Which one to use?
Use the Population setting if your data includes every member of the group you are studying (e.g., the heights of every student in a single classroom). Use the Sample setting if your data represents a random selection from a larger group (e.g., the heights of 10 students used to estimate the average of the whole school).
function calculateDeviation() {
var input = document.getElementById("dataInput").value;
var errorDiv = document.getElementById("errorMessage");
var resultsDiv = document.getElementById("results");
// Reset displays
errorDiv.style.display = "none";
resultsDiv.style.display = "none";
// Clean input data
var cleanInput = input.replace(/,/g, ' ');
var strArray = cleanInput.trim().split(/\s+/);
var numArray = [];
for (var i = 0; i < strArray.length; i++) {
var num = parseFloat(strArray[i]);
if (!isNaN(num)) {
numArray.push(num);
}
}
// Validation
if (numArray.length < 2) {
errorDiv.innerText = "Please enter at least two valid numbers to calculate deviation.";
errorDiv.style.display = "block";
return;
}
// Calculation logic
var n = numArray.length;
var sum = 0;
for (var j = 0; j < n; j++) {
sum += numArray[j];
}
var mean = sum / n;
var squareDiffs = 0;
for (var k = 0; k < n; k++) {
var diff = numArray[k] – mean;
squareDiffs += Math.pow(diff, 2);
}
var isSample = document.querySelector('input[name="calcType"]:checked').value === "sample";
var divisor = isSample ? (n – 1) : n;
var variance = squareDiffs / divisor;
var standardDeviation = Math.sqrt(variance);
// Display Results
document.getElementById("resCount").innerText = n;
document.getElementById("resMean").innerText = mean.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4});
document.getElementById("resVariance").innerText = variance.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4});
document.getElementById("resSD").innerText = standardDeviation.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4});
resultsDiv.style.display = "block";
}