Standard Deviation Calculator
Calculate mean, median, mode, variance, standard deviation, and more from your data set.
How to Calculate
σ = √(Σ(xᵢ - μ)² / N) | s = √(Σ(xᵢ - x̄)² / (n-1))
Population standard deviation (σ) divides by N, the total count. Sample standard deviation (s) divides by n-1 (Bessel's correction) to provide an unbiased estimate from a sample.
Frequently Asked Questions
What is standard deviation?
Standard deviation measures how spread out numbers are from the mean. A low standard deviation means data points are close to the average; a high standard deviation means they are spread out.
Population vs sample standard deviation?
Use population standard deviation when your data includes the entire group. Use sample standard deviation when your data is a sample from a larger population. The sample version divides by n-1 instead of n.
What is the empirical rule?
The empirical rule states that in a normal distribution: 68% of data falls within 1 standard deviation, 95% within 2, and 99.7% within 3 standard deviations of the mean.
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