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Standard Deviation Calculator

Sample & Population Variance and Mean
Supports any list of numbers (e.g. 5, 8, 12, 14, 18, 22).
Presets:
Step-by-Step Deviation Table (x - x̄)²
# Value (x) Deviation (x - x̄) Squared (x - x̄)²
Statistical Results
Sample Standard Deviation (s)
s = 5.24
Sample Variance (s²): 27.41
Population Standard Deviation (σ)
σ = 4.90
Population Variance (σ²): 23.98
Mean (Average x̄):18.00
Count (N):8
Sum (Σx):144.00
Sum of Squares Σ(x - x̄)²:191.88
Standard Error (SE):1.85

Frequently Asked Questions

Population Standard Deviation (σ): Used when you have data for the entire population. Divides by N: σ = √[Σ(x − μ)² / N].
Sample Standard Deviation (s): Used when estimating the population from a smaller sample subset. Uses Bessel's correction and divides by n − 1: s = √[Σ(x − x̄)² / (n − 1)].

Variance is simply the square of standard deviation: Variance = (Standard Deviation)². It measures the average squared deviation of each number from the mean.