SD vs. standard error?

SD describes individual data; standard error describes an estimate like the sample mean.

Standard deviation

➗ Mathematics & Statistics By CampusDown Wiki Editorial Team Last updated October 26, 2026

Standard deviation measures how spread out data values are around their mean.

Contents

1. How to calculate it
2. Interpreting it
3. FAQ
4. References

How to calculate it

Subtract the mean from each value, square the differences, and average them to get the variance; its square root is the standard deviation. For 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5, the variance 4, and the SD 2. When estimating from a sample, divide by n−1 instead of n (Bessel's correction), because the sample mean hugs the sample and understates spread.

Interpreting it

For a normal distribution, about 68% of values fall within ±1σ, 95% within ±2σ, and 99.7% within ±3σ. SD underlies z-scores, Six Sigma quality control, and stock volatility. The spread of a sample mean, the standard error σ/√n, connects to the central limit theorem and p-values.

FAQ

What does an SD of zero mean?: Every value is identical.
SD vs. standard error?: SD describes individual data; standard error describes an estimate like the sample mean.

Sources reviewed: 2026-10-26

References

Wasserman, L. (2004). All of Statistics. Springer.
Freedman, D., Pisani, R., & Purves, R. (2007). Statistics (4th ed.). W. W. Norton.

Reports and materials that use this theory (Korean)

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This article was last updated on October 26, 2026. It is based on widely recognized original works and textbooks; when citing it in a paper, please check the original sources listed in the references.