12/28/2023
8 min read
Summary statistics collapse many numbers into a few interpretable values. Each summary hides assumptions—especially about outliers and distribution shape.
**Mean** traces the arithmetic balance point but shifts heavily when one value is extreme. **Median** tracks the middle rank and resists outliers yet discards magnitude information. **Variance** averages squared deviations from the mean; **standard deviation** restores units by taking the square root. When calculators offer sample vs population formulas (ddof), choose sample estimators when data are a subset of a larger reality.
Mean x̄ = Σx / n. Sample variance s² = Σ(x − x̄)² / (n − 1) for unbiased estimation when data represent a sample.
Incomes {30k, 35k, 40k, 200k}: mean ≈ 76k but median ≈ 37.5k—the median better reflects the typical earner while the mean follows the millionaire spike.
Paste or type your data into the Mean calculator (or related statistics tool), choose sample versus population if prompted, then interpret mean together with spread. Export or note outliers separately when they dominate the mean.
Population formulas divide variance by n; sample formulas divide by n − 1 to correct bias when estimating an unknown population from limited rows.
It measures spread around the mean for roughly bell-shaped data. Skewed or bounded data often needs percentiles or domain-specific risk metrics.
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