Standard Deviation Calculator
Sample & Population Variance and MeanStep-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
• Sample Standard Deviation (s): Used when estimating the population from a smaller sample subset. Uses Bessel's correction and 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.