Standard Deviation Calculator
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
line-height: 1.6;
margin: 0;
padding: 20px;
background-color: #f8f9fa;
color: #333;
}
.calculator-container {
max-width: 800px;
margin: 20px auto;
background-color: #fff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
border: 1px solid #e0e0e0;
}
h1, h2 {
color: #004a99;
text-align: center;
margin-bottom: 20px;
}
.input-section, .result-section, .article-section {
margin-bottom: 30px;
padding: 25px;
border-radius: 6px;
background-color: #fdfdfd;
border: 1px solid #eee;
}
.input-group {
margin-bottom: 15px;
display: flex;
flex-wrap: wrap;
align-items: center;
}
.input-group label {
flex: 1 1 150px; /* Responsive label width */
margin-right: 15px;
font-weight: 600;
color: #555;
}
.input-group input[type="text"],
.input-group input[type="number"] {
flex: 2 1 200px; /* Responsive input width */
padding: 10px 12px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1rem;
box-sizing: border-box; /* Include padding and border in the element's total width and height */
}
button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #004a99;
color: white;
border: none;
border-radius: 5px;
font-size: 1.1rem;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 10px;
}
button:hover {
background-color: #003366;
}
#result {
text-align: center;
font-size: 1.8rem;
font-weight: bold;
color: #28a745;
background-color: #e9f7ec;
padding: 15px;
border-radius: 6px;
border: 1px solid #28a745;
margin-top: 20px;
}
.article-section h2 {
text-align: left;
margin-bottom: 15px;
}
.article-section p, .article-section ul, .article-section li {
margin-bottom: 15px;
}
.article-section li {
margin-left: 20px;
}
.error-message {
color: red;
font-weight: bold;
text-align: center;
margin-top: 15px;
}
@media (max-width: 600px) {
.input-group {
flex-direction: column;
align-items: stretch;
}
.input-group label {
margin-bottom: 8px;
margin-right: 0;
}
.input-group input[type="text"],
.input-group input[type="number"] {
width: 100%;
margin-right: 0;
}
button {
font-size: 1rem;
}
#result {
font-size: 1.5rem;
}
}
Standard Deviation Calculator
Understanding Standard Deviation
Standard deviation is a crucial statistical measure that quantifies the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (average) of the set, while a high standard deviation indicates that the values are spread out over a wider range. It's a fundamental tool in finance, science, quality control, and many other fields for understanding data variability.
How to Calculate Standard Deviation
The calculation involves several steps:
- 1. Calculate the Mean (Average): Sum all the data points and divide by the number of data points.
- 2. Calculate Deviations from the Mean: For each data point, subtract the mean from it.
- 3. Square the Deviations: Square each of the differences calculated in the previous step.
- 4. Calculate the Variance: Sum all the squared deviations. Then, divide this sum by the number of data points (for population standard deviation) or by (the number of data points – 1) (for sample standard deviation). This calculator computes the sample standard deviation, which is more common when analyzing a subset of data.
- 5. Calculate the Standard Deviation: Take the square root of the variance.
Formula for Sample Standard Deviation (s):
$ s = \sqrt{\frac{\sum_{i=1}^{n}(x_i – \bar{x})^2}{n-1}} $
Where:
- $s$ is the sample standard deviation
- $x_i$ is each individual data point
- $\bar{x}$ is the mean of the data points
- $n$ is the number of data points
- $\sum$ denotes the sum
When is Standard Deviation Used?
Standard deviation is widely applied across various disciplines:
- Finance: To measure the volatility of an investment or asset. Higher standard deviation implies higher risk.
- Science: To assess the reliability and reproducibility of experimental results.
- Quality Control: To monitor consistency in manufacturing processes.
- Social Sciences: To understand the spread of survey responses or demographic data.
- General Data Analysis: To describe the dispersion of any numerical dataset.
By understanding standard deviation, you gain deeper insights into the nature and variability of your data.
function calculateStandardDeviation() {
var dataInput = document.getElementById("dataPoints").value;
var resultDiv = document.getElementById("result");
var errorMessageDiv = document.getElementById("errorMessage");
resultDiv.innerHTML = ""; // Clear previous results
errorMessageDiv.innerHTML = ""; // Clear previous errors
// Process the input string into an array of numbers
// Split by comma or space, filter out empty strings and convert to float
var dataPointsArray = dataInput.split(/[\s,]+/).filter(function(item) {
return item.trim() !== "";
}).map(function(item) {
return parseFloat(item);
});
// — Input Validation —
if (dataPointsArray.length < 2) {
errorMessageDiv.innerHTML = "Please enter at least two data points.";
return;
}
for (var i = 0; i < dataPointsArray.length; i++) {
if (isNaN(dataPointsArray[i])) {
errorMessageDiv.innerHTML = "Invalid input. Please ensure all entries are numbers.";
return;
}
}
// — Calculation Steps —
// 1. Calculate the Mean
var sum = 0;
for (var i = 0; i < dataPointsArray.length; i++) {
sum += dataPointsArray[i];
}
var mean = sum / dataPointsArray.length;
// 2. Calculate Squared Deviations from the Mean
var squaredDeviations = [];
for (var i = 0; i < dataPointsArray.length; i++) {
var deviation = dataPointsArray[i] – mean;
squaredDeviations.push(deviation * deviation);
}
// 3. Calculate the Variance (using n-1 for sample standard deviation)
var sumSquaredDeviations = 0;
for (var i = 0; i < squaredDeviations.length; i++) {
sumSquaredDeviations += squaredDeviations[i];
}
// Ensure we don't divide by zero if n=1, though handled by initial check
var variance = sumSquaredDeviations / (dataPointsArray.length – 1);
// 4. Calculate the Standard Deviation
var standardDeviation = Math.sqrt(variance);
// Display the result
resultDiv.innerHTML = "Standard Deviation: " + standardDeviation.toFixed(4); // Display with 4 decimal places
}