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What is Standard Deviation?
Standard deviation measures how spread out numbers are in a dataset. A low SD means data points cluster close to the mean; a high SD means they are spread far apart.
Population σ is used when you have the entire population. Sample s is used when your data is a sample (divides by n−1 instead of n — Bessel's correction).
Frequently Asked Questions
Standard deviation measures how spread out values are from the mean. A low standard deviation means values cluster closely around the average; a high one means they're spread widely. It's one of the most important statistics in data analysis.
Population standard deviation (σ) is used when you have data for an entire population. Sample standard deviation (s) is used when your data is a sample from a larger population — it divides by n−1 instead of n to correct for bias. When in doubt, use sample standard deviation.
Variance is the square of the standard deviation (σ² or s²). It measures average squared deviation from the mean. Standard deviation is more interpretable because it's in the same units as the data; variance is used in many statistical calculations.
High standard deviation indicates high variability — the data points are spread far from the mean. In finance, high standard deviation means high volatility (risk). In manufacturing, it means inconsistent output quality. In test scores, it means a wide range of performance.