Standard Deviation Calculator
Calculate population and sample standard deviation, variance, and mean. Enter your data as comma-separated numbers.
Enter numbers separated by commas, spaces, or new lines
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Standard Deviation
Sample SD (n-1)
Statistical Summary
Count (n)
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Sum
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Mean (Average)
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Variance
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Min / Max
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Range
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Standard Deviation Formula
Population SD (σ): σ = √[Σ(x - μ)² / N]
Sample SD (s): s = √[Σ(x - x̄)² / (n-1)]
Where:
- μ = population mean
- x̄ = sample mean
- N = population size
- n = sample size
- Σ = sum of values
What Does Standard Deviation Mean?
- Small SD = Data points are close to the mean (consistent data)
- Large SD = Data points are spread out (varied data)
- SD = 0 = All values are identical
- 68-95-99.7 Rule: 68% of data falls within 1 SD of mean in normal distribution
Example Calculation
Data: 10, 12, 23, 23, 16, 23, 21, 16
Mean: 18
Deviations: -8, -6, 5, 5, -2, 5, 3, -2
Squared: 64, 36, 25, 25, 4, 25, 9, 4
Sample SD: √(192/7) = 5.24
Population SD: √(192/8) = 4.90
Standard Deviation Interpretation Guide
| Coefficient of Variation (CV) | Interpretation |
|---|---|
| CV < 15% | Low variability - Data is consistent and reliable |
| 15% ≤ CV < 30% | Moderate variability - Acceptable for many applications |
| 30% ≤ CV < 50% | High variability - Data has significant spread |
| CV ≥ 50% | Very high variability - Data is highly inconsistent |
Note: Coefficient of Variation (CV) = (Standard Deviation / Mean) × 100%