Stdev Calculator

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Standard Deviation Calculator

Statistical Summary

Standard Deviation (σ/s):
Variance (σ²/s²):
Mean (μ/x̄):
Count (n):
Sum:
Sum of Squares:

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

Choosing the right calculation type is critical for accuracy:

  • Population Standard Deviation: Used when you have data for every member of the group you are studying (e.g., test scores for every student in a specific classroom).
  • Sample Standard Deviation: Used when your data is a random selection from a larger group (e.g., survey results from 100 people used to estimate the behavior of an entire city). It uses "Bessel's correction" (n-1) to account for bias.

Step-by-Step Example

Imagine you have the dataset: 4, 8, 6.

  1. Find the Mean: (4+8+6) / 3 = 6.
  2. Subtract the Mean from each number and square the result:
    (4-6)² = 4
    (8-6)² = 4
    (6-6)² = 0
  3. Sum the Squares: 4 + 4 + 0 = 8.
  4. Find Variance: 8 / (3-1) = 4 (for Sample).
  5. Square Root: √4 = 2. The Standard Deviation is 2.
function calculateStandardDeviation() { var rawInput = document.getElementById("dataset").value; var calcType = document.querySelector('input[name="calcType"]:checked').value; // Clean input: replace commas with spaces, then split by whitespace var cleanInput = rawInput.replace(/,/g, ' '); var numbers = cleanInput.trim().split(/\s+/).map(Number); // Filter out non-numbers var data = []; for (var i = 0; i < numbers.length; i++) { if (!isNaN(numbers[i]) && rawInput.trim() !== "") { data.push(numbers[i]); } } if (data.length < 2) { alert("Please enter at least two numbers to calculate standard deviation."); return; } // 1. Calculate Sum var sum = 0; for (var j = 0; j < data.length; j++) { sum += data[j]; } // 2. Calculate Mean var mean = sum / data.length; // 3. Sum of Squared Differences var sumOfSquares = 0; for (var k = 0; k < data.length; k++) { sumOfSquares += Math.pow(data[k] – mean, 2); } // 4. Variance var variance; if (calcType === "population") { variance = sumOfSquares / data.length; } else { variance = sumOfSquares / (data.length – 1); } // 5. Standard Deviation var stdev = Math.sqrt(variance); // Display results document.getElementById("res-stdev").innerText = stdev.toLocaleString(undefined, {minimumFractionDigits: 4, maximumFractionDigits: 4}); document.getElementById("res-variance").innerText = variance.toLocaleString(undefined, {minimumFractionDigits: 4, maximumFractionDigits: 4}); document.getElementById("res-mean").innerText = mean.toLocaleString(undefined, {minimumFractionDigits: 4, maximumFractionDigits: 4}); document.getElementById("res-count").innerText = data.length; document.getElementById("res-sum").innerText = sum.toLocaleString(); document.getElementById("res-sos").innerText = sumOfSquares.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById("stdev-results").style.display = "block"; }

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