| Describes | Dispersion around the mean |
|---|---|
| Unit | Same as the data |
| Is not equivalent to | Confidence interval |
Definition and context
Standard deviation summarizes variation based on distances from the mean, squared as part of its calculation. Its expression depends on whether we are describing a population or estimating from a sample. The final square root returns the data's unit.
Two groups can share a mean and show different standard deviations. When interpreting results, we need to know which group is being summarized and which formula was used. We should not confuse this measure of variation among observations with a standard error or a confidence interval. Although all three may appear as bars on a graph, they represent different things and need a legend explaining their meaning.
What we know and its limits
Introductory reference sheet. Properties and applications depend on measurement conditions; consult the sources before making comparisons.
Follow the evidence
The original sources for exploring this explanation and its limits.
- Introductory Statistics 2e · Measures of Spread
OpenStax · Rice University
Spread, variance, and standard deviation. - Engineering Statistics Handbook · Measures of Scale
NIST / SEMATECH
Measures of spread and sensitivity to extreme values.
Image credits
SciClue · AI-generated illustration (OpenAI) · Original source · Recurso editorial de SciClue · generado con IA