Standard Deviation Calculator
A standard deviation calculator computes population and sample standard deviation (σ and s), variance, and mean from a dataset. By calculating root-mean-square deviations, it quantifies data dispersion, proving how tightly individual data points cluster around the average in statistical analysis.
By Daniel Okoro (Mathematics Editor) · Reviewed by Maya ChenUpdated · Published
10 data points entered
Load Sample:
MEAN (AVERAGE)
Median midpoint is 8.00, Mode frequency is 8.
Sample Std Dev (s):3.433
Variance (s²):11.79
Range (Max - Min):11
Sum (Σx):77
How Does the Standard Deviation Calculator Work?
- Enter comma or space-separated numbers.
- Computes the mean and squared differences from the mean.
- Provides both sample standard deviation and population standard deviation.
What Is the Standard Deviation Formula?
s = √[ Σ(x - x̄)² / (n - 1) ] ; σ = √[ Σ(x - μ)² / N ]
Square root of the average squared deviations from the dataset mean.
Variables
s:Sample standard deviation
σ:Population standard deviation
How Do You Calculate Standard Deviation Step by Step?
Dataset: 10, 12, 23, 23, 16, 23, 21, 16Data: 10, 12, 23, 23, 16, 23, 21, 16
Count n = 8, Mean = 18.0
Sum of squared differences: 160
Sample Variance s² = 160 / 7 = 22.86
Sample Standard Deviation s = √22.86 = 4.78
Final Solution:Sample SD: 4.78 (Variance: 22.86)
Population vs sample standard deviation
| Type | Divides by | When to use |
|---|---|---|
| Population | N | You measured the entire group |
| Sample | n - 1 | You measured a sample of a larger group |
Standard Deviation Questions and Answers
Use sample standard deviation (n-1) when your data represents a sample of a larger group. Use population standard deviation (N) only when your data includes every single member of the entire group.
Where Do These Standard Deviation Standards Come From?
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