Calculate Std Deviation

Standard Deviation Calculator

Results

Count (n): –

Sum: –

Mean (μ/x̄): –

Variance (σ²/s²): –

Standard Deviation: –

function calculateSD() { var input = document.getElementById('dataInput').value; var type = document.querySelector('input[name="sdType"]:checked').value; var resultDiv = document.getElementById('sdResult'); var errorDiv = document.getElementById('errorMsg'); errorDiv.style.display = 'none'; resultDiv.style.display = 'none'; // Clean input: remove commas, replace with spaces, then split and filter var rawNumbers = input.replace(/,/g, ' ').split(/\s+/); var numbers = []; for (var i = 0; i < rawNumbers.length; i++) { var val = parseFloat(rawNumbers[i]); if (!isNaN(val)) { numbers.push(val); } } if (numbers.length < 2) { errorDiv.innerText = "Please enter at least two valid numbers."; errorDiv.style.display = 'block'; return; } // Calculation Logic var count = numbers.length; var sum = 0; for (var j = 0; j < numbers.length; j++) { sum += numbers[j]; } var mean = sum / count; var sumSquaredDiffs = 0; for (var k = 0; k < numbers.length; k++) { sumSquaredDiffs += Math.pow(numbers[k] – mean, 2); } var variance; if (type === 'sample') { variance = sumSquaredDiffs / (count – 1); } else { variance = sumSquaredDiffs / count; } var stdDev = Math.sqrt(variance); // Display Results document.getElementById('resCount').innerText = count; document.getElementById('resSum').innerText = sum.toLocaleString(undefined, {maximumFractionDigits: 4}); document.getElementById('resMean').innerText = mean.toLocaleString(undefined, {maximumFractionDigits: 4}); document.getElementById('resVariance').innerText = variance.toLocaleString(undefined, {maximumFractionDigits: 6}); document.getElementById('resSD').innerText = stdDev.toLocaleString(undefined, {maximumFractionDigits: 6}); resultDiv.style.display = 'block'; }

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Understanding Standard Deviation

Standard deviation is a statistical measure that quantifies 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 (average), while a high standard deviation indicates that the data points are spread out over a wider range of values.

Sample vs. Population Standard Deviation

Choosing the correct calculation method is critical for accuracy:

• Population Standard Deviation (σ): Used when you have data for every single member of the group you are studying (e.g., the heights of every student in a specific classroom).
• Sample Standard Deviation (s): Used when your data is a subset of a larger population (e.g., the heights of 10 students used to estimate the average height of the entire school). It uses Bessel's correction (dividing by n-1 instead of n) to provide an unbiased estimate.

The Step-by-Step Calculation

1. Calculate the Mean: Add all numbers together and divide by the total count.
2. Subtract the Mean: For each number in the set, subtract the mean and square the result. Squaring ensures that negative differences don't cancel out positive ones.
3. Calculate Variance: Find the average of those squared differences. (For a sample, divide by the count minus one).
4. Square Root: Take the square root of the variance to return the value to the original unit of measurement.

Real-World Example

Imagine you are measuring the height of five plants in centimeters: 12, 15, 12, 18, and 20.

• Mean: (12+15+12+18+20) / 5 = 15.4 cm
• Squared Differences from Mean:
  (12-15.4)² = 11.56
  (15-15.4)² = 0.16
  (12-15.4)² = 11.56
  (18-15.4)² = 6.76
  (20-15.4)² = 21.16
• Sum of Squares: 51.2
• Sample Variance: 51.2 / (5-1) = 12.8
• Standard Deviation: √12.8 ≈ 3.58 cm

Why Is This Important?

In finance, standard deviation is used as a proxy for risk; a stock with a high standard deviation is more volatile. In manufacturing, it is used in quality control to ensure products meet consistent specifications. In science, it helps researchers determine if their experimental results are significant or just due to random chance.