What Is a Standard Deviation Calculator?
A standard deviation calculator measures the amount of variation or dispersion in a dataset. A low standard deviation indicates that data points cluster near the mean, while a high standard deviation indicates wide spread. This statistic is fundamental in quality control, finance, scientific research, and data analysis.
How to Use This Standard Deviation Calculator
- Enter your data values separated by commas, spaces, or newlines in the input field.
- Click Calculate to compute the results.
- Review both population (σ) and sample (s) standard deviations, along with variance, mean, count, and each value's deviation from the mean.
Key Concepts
Standard deviation is the square root of variance. For a population: σ = √(Σ(xi − μ)² ⁄ N). For a sample: s = √(Σ(xi − x̄)² ⁄ (n − 1)), where the n − 1 denominator (Bessel's correction) compensates for sample bias. In a normal distribution, approximately 68% of data falls within 1σ of the mean, 95% within 2σ, and 99.7% within 3σ (the 68-95-99.7 rule).
σ = √(Σ(x − μ)2 ÷ N)
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population standard deviation (σ) uses N in the denominator and is used when you have data for the entire population. Sample standard deviation (s) uses n − 1 (Bessel's correction) and is appropriate when working with a subset of the population to avoid underestimating variability.
What does a standard deviation of zero mean?
A standard deviation of zero means all data values are identical—there is no variation whatsoever. Every data point equals the mean.
How is standard deviation used in finance?
In finance, standard deviation measures the volatility of asset returns. Higher standard deviation indicates greater risk. It is a key component in portfolio theory, the Sharpe ratio, and value-at-risk (VaR) calculations.