Standard Deviation Calculator
Calculate the mean, variance, and standard deviation (both population and sample) for any set of numbers.
Statistical Results
Mean (Average):
Mean = Σx / n
Population Variance (when data is the entire population):
σ² = Σ(x - mean)² / n
Sample Variance (when data is a sample from a larger population):
s² = Σ(x - mean)² / (n - 1)
Standard Deviation is the square root of variance:
σ = √(σ²) (population) or s = √(s²) (sample)
When to use which:
- Population: You have data for every member of the group
- Sample: You have a subset and want to estimate the full group