Standard Deviation Calculator
Calculate standard deviation, variance, and visualize your data distribution
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Results
Standard Deviation
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Variance
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Mean
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Data Points
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Data Visualization
Statistics Summary
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About Standard Deviation
What is Standard Deviation?
Standard deviation is a measure of 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.
Sample vs Population
When calculating standard deviation, it’s important to distinguish between a sample and a population:
- Sample: Use when your data is a subset of a larger population
- Population: Use when your data includes all members of a population
Formulas
Sample Standard Deviation:
s = √[Σ(xi – x̄)² / (n – 1)]
Population Standard Deviation:
σ = √[Σ(xi – μ)² / N]
Where:
- s = sample standard deviation
- σ = population standard deviation
- xi = each value in the dataset
- x̄ = sample mean
- μ = population mean
- n = number of data points in sample
- N = number of data points in population