📏 Standard Deviation Calculator

Standard Deviation Interpretation Framework

Quick structure to compute and interpret variability reliably.

1. Core Formulas

2. Minimal Workflow

1. Clean data (remove obvious entry errors; flag outliers, don’t auto‑delete).
2. Decide scope: full population (divide by N) or sample (n−1).
3. Compute mean, squared deviations, variance, then sqrt.
4. Report: mean, (σ or s), n, any exclusions.
5. Optionally coefficient of variation: CV = (σ / |mean|)×100% (scale comparison).

3. Interpretation Heuristics

• Compare σ to tolerance/target band, not just its magnitude.
• Stable process: recent σ within control vs historical baseline.
• Use CV when units differ or scale changes over time.

4. Quality / Sanity Checks

• σ=0? All values identical or rounding collapsed detail.
• Huge σ with small n: likely outlier dominance; examine boxplot.
• Mean near 0 inflates CV—interpret cautiously.

5. Extensions

• Weighted σ for frequency / importance: use weights sum.
• Pooled σ for two similar‑variance groups: √(((n1−1)s1²+(n2−1)s2²)/(n1+n2−2)).
• Rolling σ (window) for volatility / drift detection.

6. Common Pitfalls

• Using population formula on a sample (biases low).
• Ignoring non‑normality: σ summarises spread, not shape.
• Comparing σ across different units/scales directly.

7. Quick Reference

8. FAQ

• Variance vs σ? Variance is squared units; σ returns original units.
• When CV? Comparing variability across different scales or units.
• Outliers? Report both with and without if impactful.

9. Action Tip

Log the exact data filter & formula choice (population vs sample) beside reported σ—eliminates ambiguity later.