Standard deviation measures how spread out data is from the mean. Low SD means data clusters near the mean; high SD means it's spread widely. It's the square root of variance and is expressed in the same units as the data, making it intuitive to interpret.
How to Use
Enter your data:
- Input: Comma or space-separated numbers
- Type: Population (σ) or Sample (s)
- Results: SD, variance, Z-scores, confidence intervals
The Formulas
- Population: σ = √(Σ(x−μ)²/N)
- Sample: s = √(Σ(x−x̄)²/(n−1))
- Variance: σ² or s² (SD squared)
- CV: (SD/mean) × 100%
Population vs Sample
Population SD (σ) divides by N. Sample SD (s) divides by n−1 (Bessel's correction) to give an unbiased estimate. Use sample when working with a subset of data.
Step-by-Step Instructions
- 1Enter numbers separated by commas or spaces.
- 2Choose population or sample.
- 3View standard deviation and variance.
- 4Check Z-scores for each value.
- 5Review confidence intervals.