standard deviation concept
| Definition | The square root of the variance, the spread of a variable in its own units. Scaling a variable by a scales it by the size of a, and shifting it changes nothing. Primer S, equation S.4. |
|---|---|
| Example | A fair die has variance 2.917 and standard deviation 1.708. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id standard-deviation, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation S.4. |
| Assumptions and scope | none |
| Prior art | none recorded |
| Evidence | none |
| Reviewed | semantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation S.4.
\[\mathbb E[X]=\sum_x x\,\Pr[X=x],\qquad \operatorname{Var}(X)=\mathbb E\big[(X-\mu)^{2}\big]=\mathbb E[X^{2}]-\mu^{2},\qquad \sigma=\sqrt{\operatorname{Var}(X)}.\]
Conditions
none
Ledger
none
First stated
Primer S section S.2 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix C covers it at length.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
none
Used in
Data Mining as Observation primers L and S, chapters 3, 7, 9.
Related
variance; z-score; standard error; standardization.
See also
none
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.