Technique Masterclasses

Statistics 1

Topic Brief: Outliers Boxplots Comparing Distributions

SIGNAL Topic Master Brief — Outliers, Box Plots, and Comparing Distributions (WST01, spec 2.1/2.4)

Provenance (2026-09-29): built from research/veridian/WST01-verified-facts.md (compiled 2026-09-12, spot-check addendum 2026-09-25), re-grepped for "outlier", "box", "whisker", "fence", "quartile", "IQR", "skew" and "comparing distributions." Cross-checked against codex-deep-dive-outliers-boxplots-comparing-distributions.md (not repeated here: its fence-cascade derivation, skew-as-inequality formalisation, or full synthesis table) and signal-frequency-and-boundaries.md (a whole-Section-2 count, not the narrower figure used below). Also checked the live lesson outliers-boxplots-comparing-distributions.ts (both its worked chains, neither reproduced here) and question-bank/wst01.ts (one existing item, cited not duplicated). No new PDF fetches were made.

New here, not in CODEX's own table: the reading-and-comparing-distributions.ts audit trail (2026-09-12) records that Jun 2024 Q1's parts (c) [outlier detection], (d) [box-plot construction] and (f) [a box-plot-driven inequality] also test this sub-topic, alongside the already-documented part (e). The facts bank confirms these parts exist and their topic identity, but carries no specific quoted examiner-report detail for them — flagged below as confirmed-present-but-undetailed.

1. Frequency — seen in 5 of 6 series checked

Six WST01 series have a fully-read Principal Examiner Feedback report in the facts bank: Jun 2019, Jan 2021, Oct 2021, Jun 2022, Jan 2023, Jun 2024. This sub-topic — outliers, box plots, and comparing distributions as their own tested skill, distinct from histogram-reading, mean/SD or coding — is directly evidenced in 5 of those 6: Jan 2021, Oct 2021, Jun 2022, Jun 2024, and Jun 2019. Jan 2023's report contributes confirmed content elsewhere in Section 2 (histogram reading, grouped mean, standard deviation, linear interpolation) but nothing specific to outliers, box plots, or skewness — a genuine absence from this specific sub-topic, not an unchecked gap.

2. What was tested, by series

3. Mark-tariff pattern

Two confirmed total-mark figures exist: Jan 2021 Q2 (9 marks, spanning median through box-plot construction) and Jun 2019 Q2(c) alone (7 marks, for the recompute-cascade skill only). No confirmed total exists for Oct 2021 Q3, Jun 2022 Q1, or Jun 2024 Q1, nor the exact split within Jan 2021 Q2 between its fence-finding part (c) and box-plot part (d) — flagged as open, not estimated. What is confirmed across every series checked: this sub-topic never appears as its own standalone question. It is always one part-set inside a larger opening Section-2 question, arriving after basic descriptive statistics (median, quartiles, mean, SD) and, in most series, before a comparing-distributions prose part. Where a specific mechanic is separately credited, it tends to sit at 1–3 marks per part (one fence, one whisker's placement, one "show that" listing), not as a large single block.

4. Recurring context/angle across the confirmed series

Three genuinely distinct angle-types recur, not one repeated pattern:

  1. Fence-rule application — substituting a remembered multiplier or direction for the rule the question actually gives (Jan 2021, Jun 2022). The spec's own guidance is explicit that any outlier rule will be specified in the question, so this is a self-inflicted error, not a memory-load problem.
  2. Box-plot construction and whisker mechanics — including one series' asymmetric mark-scheme credit for a whisker drawn to the fence rather than a real value (Jan 2021), and a data correction that forces both fences to be rebuilt even on the quartile that wasn't itself amended (Jun 2019).
  3. Comparing two distributions in words — confirmed in 3 of the 5 series as needing one named statistic plus its actual figure for each group, not a bare ranking claim between two different statistics (Jun 2022, Oct 2021, Jun 2024).

Jun 2024 additionally shows a fourth, less-documented angle — box-plot-driven inequality algebra — but the record currently holds only its existence, not a worked mechanism. No real-world dataset theme repeats across series (ages, log lengths, quiz scores, tree heights all appear once each); the recurrence is structural, not thematic.

5. If this topic appears, here's what to expect

Expect this content as a multi-part slice of a larger opening question, not a standalone question — typically arriving after basic descriptive statistics and before or alongside a comparing-distributions prose part. Any outlier-identification rule will be given in the question itself; the single most repeated real error across the confirmed series is substituting a remembered rule or direction instead of the one actually stated. Box-plot construction marks reward whiskers drawn to genuine data values — treat any credit for a whisker at the fence itself as a one-sided, inconsistent exception, not a second valid method. A "show that N outliers exist" instruction requires the outliers themselves to be listed, not just the fences that identify them. If a data value is amended mid-question, check whether either quartile's own value shifts before reusing old fences — both fences may need rebuilding even when only one quartile changed. A comparing-distributions prose part rewards one named statistic (median, IQR, or similar) with its actual figure for each group, not an unsupported claim about which statistic is "more accurate" or "more reliable."

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