Standard Deviation Calculator
Calculate standard deviation, variance, mean, median, and other statistics for a data set. Supports population and sample calculations.
A standard deviation calculator computes the spread of a data set by calculating sample or population standard deviation, variance, mean, and other descriptive statistics with a step-by-step breakdown.
Examples
Test Scores
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Quick Tips
- •Use sample standard deviation (n-1) when your data is a subset of a larger population.
- •Double-check your inputs — a single outlier can dramatically change the standard deviation.
- •Use the step-by-step breakdown to verify intermediate calculations.
A standard deviation calculator computes the spread of a data set by calculating sample or population standard deviation, variance, mean, and other descriptive statistics with a step-by-step breakdown.
How to Use This Calculator
Enter your data as a list of numbers separated by commas, spaces, or new lines. Select whether your data is a Population (entire group) or a Sample (subset). Click Calculate to see the standard deviation, variance, mean, and a step-by-step breakdown of the calculation.
Understanding the Formula
Sample Std Dev (s) = √[Σ(x - x̄)² / (n - 1)]. Population Std Dev (σ) = √[Σ(x - μ)² / N].
Examples
Test Scores
For scores 10, 12, 23, 23, 16, 23, 21, 16, the sample standard deviation is 5.24.
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Sample standard deviation uses n-1 in the denominator (Bessel's correction) to provide an unbiased estimate for the wider population, whereas population standard deviation uses N.
Assumptions & Limitations
- Assumes exact input values — rounding errors in the inputs will propagate to the result.
- The choice between population and sample mode must match how the data was collected; using the wrong mode produces a biased estimate.
- Results may show floating-point approximations for irrational numbers.