Standard Deviation Calculator
Calculate population or sample standard deviation and variance for any data set. Enter comma-separated numbers for instant results.
Standard Deviation
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Variance —
Mean —
Count (n) —
How to Use This Calculator
Enter your data set as comma-separated numbers (e.g. 2, 4, 4, 4, 5, 5, 7, 9). Select Population or Sample type, then view standard deviation, variance, and mean.
Formula
σ = √(Σ(x − μ)² / N) • s = √(Σ(x − x̄)² / (n−1))
Example
2,4,4,4,5,5,7,9 → Mean=5, Variance=4, σ=2.0
Frequently Asked Questions
- Standard deviation measures how spread out numbers are from the mean. A low value means data is clustered closely; a high value means it is spread widely.
- Use population (σ) when you have data for the entire group. Use sample (s) when your data is a subset, which corrects for bias using n−1.
- Variance is the square of the standard deviation (σ²). It measures the average squared distance of each data point from the mean.
- A high standard deviation means your data points are widely spread around the mean, indicating more variability or uncertainty.
- In a normal distribution: ~68% of data falls within 1σ, ~95% within 2σ, and ~99.7% within 3σ of the mean.