Standard Deviation Calculator
Calculate mean, population and sample standard deviation, variance. Comma-separated input.
How to Use
Enter your values in the fields above and click Calculate to get instant results. All computations run locally in your browser. No data is ever uploaded or stored.
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Standard Deviation and Statistical Analysis
Standard deviation measures how spread out data points are from the average. A low standard deviation means values cluster closely around the mean; a high value indicates wide dispersion. CalcSolver's standard deviation calculator computes mean, variance, and both population and sample standard deviations from any data set.
For the dataset {2, 4, 4, 4, 5, 5, 7, 9}: mean = 5, variance = 4, population standard deviation = 2. About 68% of values in a normal distribution fall within one standard deviation of the mean, and 95% fall within two.
Standard deviation is crucial in finance (measuring investment risk/volatility), quality control (monitoring manufacturing consistency), and research (assessing data reliability). Use sample standard deviation (dividing by n−1) when analyzing a subset of a larger population, and population standard deviation (dividing by n) when you have complete data. Generate random datasets with CalcSolver's random number generator for practice.
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Frequently Asked Questions
What is standard deviation?
Standard deviation measures how spread out numbers are from the mean (average). A low standard deviation means data points are close to the mean; a high value means they are spread out.
What is the difference between population and sample standard deviation?
Population standard deviation (σ) divides by N (total count). Sample standard deviation (s) divides by N-1 (Bessel's correction). Use population when you have all data, sample when you have a subset.
How do I interpret standard deviation?
In a normal distribution: about 68% of data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3. This is the empirical rule or 68-95-99.7 rule.