Standard Deviation Calculator
Calculate standard deviation, variance, and statistical measures for your data set
Enter Your Data
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Data Preview:
[10, 12, 16, 16, 21, 23, 23, 23]
8 values • Sorted from smallest to largest
Results
Sample Std Dev (s)
5.2372
Most commonly usedPopulation Std Dev (σ)4.8990
Variance (s²)27.4286
Count (n)8
Descriptive Statistics
Mean (μ)18.0000
Median18.5000
Minimum10.0000
Maximum23.0000
Range13.0000
CV (Coefficient)29.10%
Formula
s = √[Σ(x - μ)² / (n-1)]
Sample standard deviation using Bessel's correction (n-1)
Understanding Standard Deviation
Standard deviation measures how spread out numbers are from their average (mean). A low standard deviation means values are close to the mean, while a high standard deviation means values are spread out over a wider range.
Sample vs Population
- Sample Standard Deviation (s): Use when your data is a sample from a larger population. Divides by (n-1) for unbiased estimate. Most common in practice.
- Population Standard Deviation (σ): Use when you have the entire population. Divides by n. Used less frequently.
Interpreting Results
- • Low Std Dev: Data points cluster close to mean (consistent)
- • High Std Dev: Data points spread far from mean (variable)
- • Zero Std Dev: All values are identical
The coefficient of variation (CV) expresses standard deviation as a percentage of the mean, useful for comparing variability between different datasets.