Standard Deviation Calculator
Calculate population or sample standard deviation, variance, mean and count from a data set.
Standard Deviation Calculator
Calculate population or sample standard deviation, variance, mean and count from a data set.
How to use the Standard Deviation Calculator
- Enter numbers separated by commas, spaces, or line breaks.
- Choose "Population" or "Sample" type.
- Click Calculate.
Formula
Mean (μ) = Σx / n
Population SD (σ) = √(Σ(x−μ)² / n)
Sample SD (s) = √(Σ(x−x̄)² / (n−1))
Example
Data: 2, 4, 4, 4, 5, 5, 7, 9. Mean = 5. Sample SD ≈ 2.0.
Step-by-step calculation
- Calculate mean: (2+4+4+4+5+5+7+9)/8 = 5.
- Calculate squared differences from mean.
- Sum and divide by n (population) or n−1 (sample).
- Take the square root.
Real-world uses
- Quality control and consistency analysis.
- Financial volatility measurement.
- Scientific data analysis.
Common mistakes
- Using population formula when you have a sample (and vice versa).
- Forgetting to subtract the mean from each value.
- Using n−1 for population (use n instead).
Frequently asked questions
Population vs sample — which should I use?
Use population (σ) if your data includes ALL items of interest. Use sample (s) if it is a subset.
What does standard deviation tell you?
How spread out the data is from the mean. Low SD = data clusters near the mean.
Why divide by n−1 for samples?
This is Bessel's correction. It compensates for the bias in estimating population variance from a sample.