Technique Masterclasses

Statistics 1

Topic Brief: Reading and Comparing Distributions

SIGNAL Topic Master Brief — Reading Data Representations, and Comparing Distributions in Words (WST01, spec 2.1, plus the shared 2.1/2.4 guidance point)

Provenance (2026-09-29): built from research/veridian/WST01-verified-facts.md (compiled 2026-09-12, spot-check addendum 2026-09-25), grepped for "histogram", "stem-and-leaf", "back-to-back", and the individual series citations quoted below, plus the header/sourcing note of the live lesson content/veridian/curriculum/wst01/reading-and-comparing-distributions.ts. Cross-checked against codex-deep-dive-reading-and-comparing-distributions.md (this folder, §3's synthesis table) and signal-frequency-and-boundaries.md (this folder, whole-Section-2 "6 of 6" figure and its counting methodology) so this brief does not restate either — CODEX owns the formal derivations and worked micro-examples; this document is the exam-pattern layer on top. content/veridian/question-bank/wst01.ts was also checked: neither of its two entries touches this topic. No new PDF fetches were made.

1. Frequency — seen in 4 of 6 series checked

The facts bank has a fully-read examiner report for 6 of WST01's 14 series: Jun 2019, Jan 2021, Oct 2021, Jun 2022, Jan 2023, Jun 2024. This topic — reading a histogram or stem-and-leaf diagram, and/or comparing two distributions in words — is directly evidenced in 4 of those 6: Jan 2023, Jun 2022, Oct 2021, Jun 2024. It is not confirmed for Jun 2019 or Jan 2021; both series' opening Section-2 question is owned entirely by the sibling outliers/box-plot topic, with no citation in the facts bank touching diagram-reading or the compare-in-words step for either sitting.

That "4 of 6" bundles two sub-skills that do not always co-occur, and splitting them is more honest than one combined count:

Jun 2024 is the only series confirmed on both counts. A fifth citation, Jun 2024 Q1(a), is real but is a question-paper-and-mark-scheme find with no examiner-report quote attached, so — following this course's own counting convention (see signal-frequency-and-boundaries.md §1) — it does not change either "of 6" figure above; it is noted in §2 as an additional, differently-sourced data point.

2. What was actually tested, by series

3. Mark-tariff pattern

Two hard numbers exist in the reviewed record: Jun 2024 Q1(a) is worth 1 mark (a single B1, "cao"), and Q1(b) on the same paper is worth 3 marks. Beyond that, the archive does not break out this topic's own share cleanly — Jan 2023's whole Q1 (histogram-reading plus three other Section-2 sub-topics) carries 10 of the paper's 75 marks in total, but no source read for this brief states part (a)'s individual value inside that 10. No mark value for the "compare two distributions" sub-part itself was located in any of its three confirmed series; that is stated here as an open gap, not filled with a plausible guess.

What is confirmed is position: in 3 of the 4 contributing series — Jan 2023, Jun 2022, Jun 2024 — this content sits inside Q1, the paper's opening question. Oct 2021 is the one exception, where the equivalent content sits inside Q3 instead. The topic's default slot is "first question on the paper," confirmed in 3 of 4 series rather than as a fixed rule.

4. Recurring context/angle across the four series

One structural invariant holds across every series that tests the compare-in-words step, regardless of which question number it falls under: it is never a standalone question. It is always the final sub-part of whatever multi-part Section-2 data-representation question that series happens to build — after a histogram in some sittings, after a stem-and-leaf diagram in others, after box-plot/outlier work in Oct 2021's case. The representation changes; the closing "now compare them in words" part does not move away from being that question's last part.

The three confirmed compare-in-words failures also share one root cause dressed in three different surface forms — an unstructured prose answer rather than the disciplined named-statistic / both-figures / stated-direction routine the mark scheme actually rewards: Jun 2022's version substitutes mean for median with no justification; Jun 2024's version names a statistic but drops the figures; Oct 2021's version answers the wrong question (similarity instead of difference). That is a single skill failure, not three unrelated ones.

Diagram-reading errors sit on a different axis, worth keeping distinct from the compare-in-words failures above: Jan 2023's is a substitution error (height standing in for area), Jun 2024's is a directional error (which flank is which). Neither is a prose-structuring problem, so the fix for one does not transfer to the other or to the compare-in-words fix.

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

Expect this content early — most likely opening the paper as part of Q1 — built on whichever data representation that series has chosen (histogram, ordinary stem-and-leaf, or back-to-back stem-and- leaf), and expect its last sub-part to ask for a written comparison of two groups. For the reading step: check a histogram's axis is frequency density before reading any bar, and on a back-to-back diagram, work out which flank reads towards the stem and which reads away from it before assigning ranks. For the comparison step: commit to one named statistic, quote both groups' actual figures for it, and state which way the difference runs — every confirmed failure across all three series is a version of skipping one of those three components, not a computational slip.

Sources and limitations