Standard Deviation Explained — Measuring the Spread of Your Data
Standard deviation quantifies how spread out data values are around their mean. A low standard deviation means values cluster tightly around the average; a high one means they are widely scattered. It is one of the most widely used statistics in science, finance, engineering, and social research because it summarizes data variability in a single interpretable number measured in the same units as the original data.
Key statistics this tool calculates:
1. Mean — The arithmetic average of all values: sum divided by count. Serves as the central reference point for all other measures.
2. Population standard deviation (σ) — Use this when your dataset IS the complete population. Divides the sum of squared deviations by N.
3. Sample standard deviation (s) — Use this when your data is a sample drawn from a larger population. Divides by N-1 (Bessel's correction) to give an unbiased estimate. This matches Excel's STDEV function.
4. Standard error (SE) — SE = s / √n. Measures how reliable the sample mean is as an estimate of the population mean. Decreases as sample size increases.
5. Margin of error (95% CI) — 1.96 × SE. The range within which the true population mean is expected to fall 95% of the time when sampling is repeated.
To use this calculator, paste your numbers separated by commas, spaces, or line breaks. Non-numeric values are automatically ignored. At least 2 data points are needed to compute the sample standard deviation and standard error.
Frequently Asked Questions
A: You need at least 1 point for the mean and population std dev. At least 2 points are required for sample std dev, standard error, and margin of error. More data generally yields more reliable statistics.
A: Yes. The sample standard deviation (s) matches Excel's STDEV/STDEV.S. The population standard deviation (σ) matches STDEVP/STDEV.P.
A: Yes, both integers and decimals are supported. For example: 3.14, 2.71, 1.41