central limit theorem concept
| Definition | The sampling distribution of a mean of n independent values is close to normal once n is a few dozen, whatever the shape of the values, with standard error sigma over the square root of n. Primer S, equation S.11. Also central limit. |
|---|---|
| Example | Eight values with standard deviation 2 have a mean with standard error 2 over root 8, which is 0.707. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id central-limit-theorem, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation S.11. |
| 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.11.
\[\operatorname{SE}(\bar x)=\frac{\sigma}{\sqrt n},\qquad \frac{\bar x-\mu}{\sigma/\sqrt n}\ \approx\ \text{normal with mean } 0 \text{ and variance } 1.\]
Conditions
none
Ledger
none
First stated
Primer S section S.4 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 primer S.
Related
normal distribution; standard error; sampling distribution; law of large numbers.
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.