Standard Deviation
Mean, variance, std dev from a list
About Standard Deviation
Standard deviation measures how spread out a dataset is around its mean. Low SD means values cluster tightly; high SD means they're scattered. It's the most-used measure of dispersion in statistics, finance, and quality control, and underpins concepts like z-scores, confidence intervals, and the empirical rule (68-95-99.7%).
Frequently asked questions
Population SD divides by N; sample SD divides by N-1 (Bessel's correction) because using the sample mean introduces a tiny bias. Use sample SD unless you genuinely have the whole population.
Variance (SD²) adds linearly across independent variables and makes some maths cleaner. SD wins on interpretability because it has the same units as the original data.
For roughly normal distributions: ~68% of values within 1 SD, ~95% within 2, ~99.7% within 3. A useful shortcut for sanity-checking results.
No — SD requires interval or ratio data. For ordinal data, use range or IQR instead.
SD is sensitive to outliers because it squares deviations from the mean. Robust alternatives (median absolute deviation) downweight extreme values.
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Standard Deviation
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