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sampling distribution concept

DefinitionThe distribution of a statistic across repeated samples of the same size, whose standard deviation is the statistic's standard error. The bootstrap estimates it from one sample. Primer S, equation S.11.
ExampleThe mean of eight values with standard deviation 2 has a sampling distribution with spread 0.707.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id sampling-distribution, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equation

Book equation S.11.

Assumptions and scopenone
Prior artnone recorded
Evidencenone
Reviewedsemantic 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

standard error; bootstrap; central limit theorem; confidence interval.

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.

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