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Guide

How to Calculate Standard Deviation and Variance

Learn what standard deviation measures, the difference between population and sample formulas, and how to read the result.

Open the Standard Deviation Calculator

Standard deviation measures how spread out a set of numbers is around the mean. A small standard deviation means the values cluster tightly; a large one means they are scattered widely.

What standard deviation tells you

Two datasets can share the same mean but have very different spreads. Standard deviation quantifies that spread in the same units as the data, making it easy to interpret: roughly two-thirds of values lie within one standard deviation of the mean in a normal distribution.

Population vs. sample

Use the population formula when your data is the entire group of interest; use the sample formula when your data is a sample drawn from a larger population. The difference is the denominator: population divides by N, sample divides by N − 1 (Bessel's correction) to give an unbiased estimate.

The formula

Variance = Σ(xᵢ − mean)² ÷ (N or N−1)

Standard deviation = √Variance

How to use the calculator

  1. Enter your numbers, separated by commas, spaces, or new lines.
  2. Choose population or sample.
  3. Read the standard deviation, variance, mean, and range.

Examples

For 2, 4, 4, 4, 5, 5, 7, 9 (mean 5): the population standard deviation is 2.0. A class with scores tightly bunched around 75 will have a small standard deviation; a class with scores from 40 to 95 will have a large one, even if both means are 75.

When a standard deviation calculator is useful

  • Analysing the spread of test scores or measurements.
  • Comparing the consistency of two processes or groups.
  • Computing statistics for reports and research.
  • Checking data quality and spotting outliers.

Put it into practice

Use the Standard Deviation Calculator right now — free, in your browser, no sign-up required.

Try the Standard Deviation Calculator

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