📈 Standard Deviation Calculator
Enter your dataset to calculate mean, variance, and standard deviation. Supports both population and sample calculations with step-by-step results.
Understanding Standard Deviation
Standard deviation (SD) measures the dispersion of data around the mean. It tells you how much individual data points typically deviate from the average.
- Low SD: Data points are close to the mean
- High SD: Data points are spread out over a wider range
Population vs Sample
| Type | Formula | When to Use |
|---|---|---|
| Population (σ) | √(Σ(x-μ)² / N) | Complete dataset |
| Sample (s) | √(Σ(x-x̄)² / (N-1)) | Sample of population |
Frequently Asked Questions
What is standard deviation?
Standard deviation measures how spread out data is from the mean. A low SD means data clusters around the mean; a high SD means data is more spread out.
When should I use sample vs population standard deviation?
Use population SD (divide by N) when you have data for the entire population. Use sample SD (divide by N-1) when you have a sample of a larger population.