Technique Masterclasses

Statistics 1

Topic Brief: Sampling Tree Diagrams Venn Diagrams

SIGNAL Topic Master Brief — Sampling, Tree Diagrams, and Venn Diagrams (WST01, spec 3.4)

Provenance (2026-09-29): built from research/veridian/WST01-verified-facts.md (compiled 2026-09-12, spot-check addendum 2026-09-25, Jan 2023 Q2(d) correction dated 2026-08-28), grepped for "sampl", "tree diagram", "venn" and the series citations quoted below (§5 Section 3, §7 topic-richness ranking, §8's audit of sampling-tree-diagrams-venn-diagrams.ts). Cross-checked against codex-deep-dive-sampling-tree-diagrams-venn-diagrams.md (this folder, §4's synthesis and frequency statement) and signal-frequency-and-boundaries.md (whole-Section-3 blanket count) so this document does not restate either — it narrows the CODEX synthesis to a revision-facing quick reference and adds the mark-tariff and recurring-context analysis neither existing document states directly. Also checked: the live lesson content/veridian/curriculum/wst01/sampling-tree-diagrams-venn-diagrams.ts (no worked example below duplicates it) and content/veridian/question-bank/wst01.ts (grepped; no item on this topic exists there). No new PDF fetches were made.

1. Frequency — seen in 2 of 6 series checked

The facts bank has a fully-read Principal Examiner Feedback report for 6 of the 14 WST01 series: Jun 2019, Jan 2021, Oct 2021, Jun 2022, Jan 2023, Jun 2024. Sampling/tree-diagram/Venn-diagram construction — this spec point's own named skill, as distinct from the conditional-probability and independence-vs-mutually-exclusive judgments those diagrams are sometimes used to test — is directly evidenced in 2 of those 6: Jun 2022 and Jan 2023. It is not confirmed for Jun 2019, Oct 2021, or Jun 2024; absence of a citation is not evidence of absence, only of an unread or different-topic question.

Two further series show a Venn diagram on the page but are not counted in the "2 of 6" above, because the mark scheme tests a different named spec point through that same picture: Jan 2021 Q1 and Oct 2021 Q1 both use a three-event Venn diagram, but every graded step on both questions is a complement/addition-law or independence/conditional-probability calculation (spec 3.1–3.3), not a construction or region-bookkeeping skill. They are genuine evidence that three-event Venn diagrams get drawn on this paper, just not evidence for this spec point's own skill separately from those.

2. What was actually tested, by series

3. Mark-tariff pattern

Only one series — Jan 2023 — gives a fully quantified mark tariff: a single 10-mark, four-part question, of which the quoted steps above account for roughly 4 of the 10 marks (2 B-marks in (a), an M1 in (c), M1+A1ft in (d)); the rest of that question isn't itemised in the source. Jun 2022's three citations (Q3(d), Q4(b), Q4(c)) each document a wrong-answer mechanism without giving that sub-part's own mark total, so no second full tariff exists to compare against. What both series agree on: this content never anchors a short, dedicated, single-skill item — it sits as one or more sub-parts (worth 1–2 marks each: a B-mark for a branch value, an M1 for a product-and-sum step, an M1/A1ft pair for a conditional-probability step) inside a larger multi-part question. No standalone mark value for "draw a tree diagram" or "read a Venn diagram" alone was found anywhere in the reviewed record.

4. Recurring context/angle across the two series

Every confirmed tree-diagram anchor here — Jun 2022 Q3(d) and Jan 2023 Q2 — is a without-replacement draw of physical countable objects (unnamed items in Q3(d); coloured marbles in Q2), never a with-replacement scenario. The spec names both with- and without-replacement sampling, but no real, confirmed with-replacement anchor for this exact spec point was found in the six examiner reports read for this facts bank — a genuine gap in the evidence, not a claim that with-replacement questions don't occur. Jan 2023's question also introduces a mechanism Jun 2022's doesn't: a physical transfer between two containers, whose mark scheme rewards two different transfer orders identically.

On the Venn-diagram side, both confirmed citations (Jun 2022 Q4(b), Q4(c)) concern the same single diagram used across two consecutive sub-parts — one a calculation on it, the next testing whether every region, including an empty one, has been written in rather than left blank. Neither citation records what real-world categories the diagram's sets represented (only the label "N" for one set survives in the quote), so no claim is made here about a recurring real-world scenario for Venn diagrams — only about the recurring error type (completeness of blank/zero regions).

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

Expect either a without-replacement tree diagram built from physical objects, most likely as several sub-parts of one larger multi-part question rather than its own short item — check the composition genuinely changes (both numerator and denominator) after every draw, and if a transfer between two containers is involved, expect credit for landing on the same rebuilt branch fractions regardless of which item arrived first. Separately, or on the same question, expect a Venn diagram where the graded risk is completeness — write every region's value, including a zero, rather than leaving it blank — and where an "assume independence by eye" shortcut is a confirmed, named trap distinct from the diagram itself. On the evidence reviewed, this topic has not been confirmed to anchor its own short, low-mark-value question; it is tested as the vehicle for multi-step sampling or set-theory calculations worth several marks in combination.

Sources and limitations