Standard Deviation Calculator

Standard deviation measures how spread out a dataset is around its mean. A small standard deviation means values cluster tightly around the average; a large one means they are more spread out. Variance is the standard deviation squared — it is calculated first, then the square root gives the standard deviation in the same units as the original data.

Use sample standard deviation (dividing by n − 1) when your data is a subset used to estimate a larger population — this is the more common case and slightly increases the result to correct for bias. Use population standard deviation (dividing by n) only when your dataset includes every member of the group you care about.

Example: for the dataset 2, 4, 4, 4, 5, 5, 7, 9 (mean = 5), the sample standard deviation is about 2.14, while the population standard deviation is about 2.00 — the sample version is always slightly larger for the same data.

Sample standard deviation (n−1 denominator) corrects bias when your data is a subset of a larger population — most spreadsheet STDEV functions use n−1 by default.

A low standard deviation means data clusters tightly; a high one means wide spread. Compare std dev only within the same unit scale as the original measurements.

Worked example with defaults in sample mode: dataset mean 5, sample std dev ≈ 2.14. Switch to population mode (n denominator) for the same data → ≈ 2.00.

Coefficient of variation (std dev ÷ mean × 100) compares spread across different units — 2.14 std dev on mean 5 is 42.8% CV, useful when comparing volatility of two datasets with different averages. CV = std/mean × 100 — 2.14 on mean 5 is 42.8% CV for comparing spread when means differ between datasets. State the coefficient-of-variation percentage when comparing datasets whose means are not equal.

Excel STDEV.S matches sample mode (n−1); STDEV.P matches population mode — verify which denominator your spreadsheet uses before comparing homework to this calculator's toggle. STDEV.S uses n−1 like sample mode here — match Excel choice before comparing spreadsheet homework to the population toggle. Circle whether you matched STDEV.S or STDEV.P before comparing spreadsheet homework results.

Adding a single outlier (100) to the default list spikes sample std dev far above 2.14 — one bad sensor reading dominates quality control charts until investigated. Adding outlier 100 to default list spikes sample std dev above 2.14 — one bad sensor reading dominates SPC charts until replaced. Flag suspected outliers in your write-up when one reading spikes spread dramatically.