Standard Deviation Calculator
Calculation Results
Population Standard Deviation (σ)
Data Points (n)
0
Sum
0
Mean (μ)
0
Variance
0
Standard Deviation
0
Data Points Analysis
| # | Data Point (xᵢ) | Deviation (xᵢ - μ) | Squared Deviation (xᵢ - μ)² |
|---|
About Standard Deviation
Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that values tend to be close to the mean, while a high standard deviation indicates values are spread out over a wider range.
Population Standard Deviation Formula (σ):
σ = √[ Σ (xᵢ - μ)² / N ]
Where: μ = population mean, N = number of data points
Sample Standard Deviation Formula (s):
s = √[ Σ (xᵢ - x̄)² / (n - 1) ]
Where: x̄ = sample mean, n = number of data points
Key differences:
- Use population standard deviation when your data represents the entire population
- Use sample standard deviation when your data is a sample of a larger population