sample variance concept
| Definition | The 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. |
|---|---|
| Example | The 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. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id sample-variance, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation S.9. |
| 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.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.