skewness concept
| Definition | The mean cubed deviation of a column from its mean over the cube of its spread, zero for a symmetric column. The hubness gate reads it. Chapter 3 section 3.5. Also skew. |
|---|---|
| Example | Counts of 1, 1, 1, 1, and 10 have a long right tail and positive skewness, and a symmetric column has zero. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id skewness, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | turboquant-pro/docs/RESULTS_strata_phase23_gates.md:1-45, lean/DataMiningAsObservation/Skewness.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- The weighted mean cubed deviation of a column from its mean over the cube of its spread. It is unchanged by a shift and by a positive rescaling, changes sign when the column is negated, and is zero for a column symmetric about its mean.
- The hubness gate reads the skew of the neighbour-count distribution, and the remedy that was to fix it moved the skew from 3.970 to 3.177 while the compressed path still failed every stratum.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 3 section 3.5 and chapter 10 section 10.2 of Data Mining
as Observation, with the hubness gate’s skew in
openvector-bench/results/R13_STAGE1_RESULT.md:75-110.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 10 section 10.5 | Gate A design error, A prime skew 3.970 to 3.177, max 287 to 213, Robin Hood 0.372 to 0.261, fraction 0.117 to 0.079, compressed path 0.663 vs 0.90, seven strata, 0.62 to 0.69 vs 0.76 to 0.84 | turboquant-pro/docs/RESULTS_strata_phase23_gates.md:1-45 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Skewness.lean,
theorems skew_shift, skew_scale,
skew_neg, skew_symmetric, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation primer S, chapters 3, 5, 10, 11.
Related
hubness; Robin Hood index; variance; gate; percentile.
See also
Book equations stated beside the entry’s terms, not defining it: 0.35, 10.3, 0.17.
Ledger rows that cite the entry’s records without naming it: NEG-14.
Sources-table rows that share a record with the entry without naming it: chapter 10 section 10.2, chapter 10 section 10.4, chapter 10 section 10.5.
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.