Standard Deviation Calculator
Calculate sample and population standard deviation with step-by-step results and visual distribution graph
Input Data
Example: 12, 15, 17, 20, 22, 25, 28, 30
Results
Frequently Asked Questions
What is standard deviation?
Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.
What's the difference between population and sample standard deviation?
Population standard deviation (σ) is used when your data represents the entire population. Sample standard deviation (s) is used when your data is a sample taken from a larger population. The calculation differs by the denominator: population uses N, while sample uses N-1 (Bessel's correction).
How do I interpret standard deviation?
Standard deviation provides insight into data variability. For normally distributed data: about 68% of values lie within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.
Why is standard deviation important?
Standard deviation is crucial for understanding data variability, assessing risk in finance, quality control in manufacturing, evaluating test scores in education, and determining statistical significance in research.