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sample variance concept

DefinitionThe average squared deviation from the sample mean with n minus 1 in the denominator, because the sample mean sits closer to its own sample than the true mean does and the deviations come out a little small. Primer S, equation S.9.
ExampleThe deviations of 2, 4, 4, 4, 5, 5, 7, 9 from 5 have squares summing to 32, so the sample variance is 32 over 7, about 4.571.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id sample-variance, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equation

Book equation S.9.

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.9.

\[\bar x=\frac1n\sum_i x_i,\qquad s^{2}=\frac{1}{n-1}\sum_i(x_i-\bar x)^{2}.\]

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

variance; standard deviation; estimator, unbiased.

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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