The median of a bimodal metric lands in the empty gap - check the distribution, and never judge swing on 3 seeds

Symptom

Years of "high swing variance" and undecidable 3-seed swing readings turned out to be one fact: the metric was bimodal all along - "历代 swing 高方差与 3-seed 不可判由此定性:一直在测双稳态系统" - and every median reported from it (e.g. 12.1 mm) described a value no seed ever produced.

Context

Concrete instances: s2e_pd-1400's 20 seeds split 2.6-4.9 mm vs 19.3-24.0 mm with zero seeds between; s1e-500 read 3.9 mm on seeds 0-2 but 23.1 mm median over 20 seeds; a 3-seed reading of 19.3 was logged as "double-peak optimism, lesson recurrence #4". The selection re-audit codified the sampling rule: "3-seed 的 swing 读数不可判点, 只能筛带,选点必须 20-seed" - 3 seeds may screen a band, only 20 seeds may pick a point.

Change

Swing (and any suspected multi-modal metric) reported as mode shares plus per-mode ranges instead of a bare median; 3-seed smoke numbers demoted to band-screening; all shipping/selection decisions moved to 20-seed batteries.

Outcome

The "swing debt" bookkeeping was reinterpreted as basin probability (see swing-bistability-damping-switch), and checkpoint selection stopped being whipsawed by which basin the first three seeds happened to fall into.

Mechanism

Central-tendency statistics presuppose unimodality; on a bimodal distribution the median tracks the mode SHARE, not any achievable behavior, and small samples alias the share entirely. Mode-aware reporting (share + per-mode stats) is the only faithful summary, and the needed sample size is set by the share resolution required.

Applies when

• a quality metric shows chronic high variance across seeds
• 3-seed smoke readings contradict 20-seed batteries
• reporting swing height, clearance, or any basin-prone metric