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Standard Deviation Calculator - Variance Calculator
Free standard deviation calculator for population and sample data. Calculate variance, mean, and measure how spread out your data is.
Standard Deviation Calculator
Calculate how spread out your data is
Results
Enter your values to see results
and click the "Calculate" button
What is Standard Deviation?
Standard deviation measures how spread out numbers are from their average (mean). A low standard deviation means values are close to the mean, while high standard deviation indicates values are spread over a wider range. It's one of the most important concepts in statistics.
How to Use This Calculator
- Enter your data set separated by commas or spaces
- Select whether this is population or sample data
- Click Calculate to see standard deviation and variance
Standard Deviation Formula
σ = √[Σ(x - μ)² / N]
Population: divide by N. Sample: divide by (N-1) for unbiased estimate. Sample formula: s = √[Σ(x - x̄)² / (n-1)]
Frequently Asked Questions
What's the difference between population and sample?
Population includes ALL members of a group. Sample is a subset used to estimate population parameters. Sample standard deviation uses (n-1) in denominator to provide unbiased estimate.
What does a high standard deviation mean?
High standard deviation means data points are spread far from the mean - more variability. Low standard deviation means data is clustered close to the mean - more consistency.
What's the relationship between variance and standard deviation?
Standard deviation is the square root of variance. Variance measures spread in squared units, while standard deviation is in the same units as the original data.
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