Standard Deviation Calculator
Calculate standard deviation, variance, and mean for a data set.
About this Tool
The Standard Deviation Calculator computes the standard deviation, variance, and mean of a set of numbers. Standard deviation is a measure of the amount of variation or dispersion of 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.
Common Use Cases
Statistical Analysis
Measure the volatility of a stock's returns or the dispersion of data in a scientific experiment.
Quality Control
Monitor the consistency of a manufacturing process by measuring the variation in product specifications.
Academic Research
Analyze the spread of data in research studies to determine the reliability of results.
Pro Tips
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Sample vs. Population
This calculator computes the 'sample' standard deviation (dividing by n-1), which is the most common type and is used when your data is a sample of a larger population.
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Interpreting the Result
A smaller standard deviation means your data points are clustered closely around the average. A larger value means they are more spread out.
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Relationship to Variance
The standard deviation is simply the square root of the variance. Variance is another measure of spread, but it's in squared units, making standard deviation often easier to interpret.