Standard Deviation Calculator

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