Technique Masterclasses

Statistics 1

Level Threshold Guide

WST01 (Statistics 1) — Level/Threshold Guide

Provenance: written 2026-09-29, built entirely on research/veridian/WST01-verified-facts.md (compiled 2026-09-12, spot-check addendum 2026-09-25) — specifically its §4 (mark-scheme conventions), §5 (per-topic verified content) and the "Per-lesson bullet-by-bullet coverage audits" section, which independently re-fetched and re-verified several primary mark schemes directly against rendered PDF page images where pdftotext garbles stacked fractions. Cross-checked against forge-exam-technique-guide.md, forge-battle-card.md, codex-formula-and-method-bank.md and signal-frequency-and-boundaries.md in this same folder to avoid restating what they already cover; where a fact below also appears in one of those documents, this document goes to the next level of granularity that one didn't (a full mark-by-mark ladder, both sides of a boundary, or the exact wording that draws the line) rather than repeating the same sentence. No new PDF fetches or web searches were performed for this document — every claim below traces to a citation already independently verified elsewhere in this course's WST01 research, cited again here by series and question number. Where the real record simply doesn't contain a threshold for something (most of the paper's B1-for-a-diagram-feature and routine M1/A1 arithmetic marks have no examiner-report or audit commentary attached), this document does not manufacture one.

What "threshold" means on this paper, and what this document refuses to do

WST01 is marked M/A/B, not by level descriptors (1–5 bands, best-fit judgements) the way an essay-marked subject is. There is no qualification-wide grade boundary data anywhere in this course's source record either — signal-frequency-and-boundaries.md §2 checked the facts bank directly for "grade boundary," "boundaries" and "raw mark" and found zero matches, and this document performed no new fetch to manufacture one. So the real, checkable "threshold" structure on this paper is not a percentage-of-marks cutoff for a grade; it is the line the mark scheme itself draws, mark by mark, between a response that earns a specific M, A or B and one that doesn't — and, chained across a whole question, the line between a partial-credit stopping point and full marks. That is what this document maps, exhaustively, using only boundaries a real mark scheme or examiner report actually states. Two hard constraints follow directly from that: no likelihood percentage is invented anywhere below (only "seen in N of M series checked"), and no grade boundary is invented either. Where a boundary below is confirmed on one series only, that is stated, not smoothed into a general rule.

Every threshold below is presented as a pair: a real (or, where marked, a mechanically identical near-miss built from the same verified mechanism) response that just misses the mark, and one that just clears it — followed by the exact mark-scheme wording the boundary itself rests on.


1. The atomic thresholds: M, A, B, and the cliffs between them

Source for the mark-type definitions themselves: the "General Instructions for Marking" boilerplate opening all 14 mark schemes reviewed, byte-for-byte identical (bar the total-marks figure) across at least 6 spot-checked directly — already summarised in forge-exam-technique-guide.md §2.1. This section goes one level deeper: what actually sits on each side of the M0/M1, A0/A1 and B0/B1 line in real, quoted responses.

1.1 M0 → M1 — the method-attempt threshold

Rule, verbatim: "A method mark is given for a correct method or an attempt at a correct method."

Real ladder, Oct 2021 Q6(a) (Normal distribution, "show that P(H > 30.8) = 0.15," 3 marks total — mark scheme verified directly against the primary PDF in the facts bank's per-lesson audit of show-that-answer-discipline.ts):

1.2 The dependent-M (DM) threshold — a second method mark contingent on the first

Same anchor, 2nd line: "2nd M1 for 1 – p (where 0.84 < p < 0.86)." This is a genuinely useful, under-appreciated fact: it is a second M mark, not the accuracy mark that intuition suggests should follow a "1 − Φ(z)" step, and its band is deliberately wide (any pp between 0.84 and 0.86 qualifies) rather than pinned to one exact table value. The facts bank's own audit of this lesson found the lesson had mislabelled this line as A1 (requiring 4-d.p. table precision) in three places before correction — a genuine, previously-live error in this course's own material, which is exactly the kind of boundary-drawn-in-the-wrong-place mistake this document exists to prevent repeating.

1.3 A0 → A1, and the reach-back cso threshold

Final line of the same anchor: "A1cso for an answer of 0.1492… or better (calc: 0.1500…) with evidence of both M's seen." Two separate thresholds are compressed into this one line:

1.4 B0 → B1 — the independent/standalone-comment threshold

B marks reward a fact, comment, or diagram feature standing alone, with no method mark to lean on — which makes them unforgiving in a different way: there is no partial credit for "the right idea, wrongly expressed," because there's no M mark upstream to catch a near-miss.

Real boundary, Jun 2022 Q2(e)(ii) (regression reliability judgement, GDP-vs-population data, no min/max range given in the question — 1 mark): credited answer, verbatim, "Unreliable as 7 000 000 is much greater than the mean population/t-bar for the 9 years," with the marking note stating explicitly: "'Extrapolation so unreliable' on its own is B0. Reference to g out of range is also B0."

1.5 ft (follow-through) — earning a mark on a value that may itself be wrong

Real boundary, Jan 2023 Q2(d) (tree-diagram conditional probability, "given all 3 same colour, find P(all green)," carried from part (c)'s own answer 61/234): "A1ft for finding the correct numerator... If the answer is incorrect then working must be shown."


2. Precision thresholds — where the same rounded value sits on different sides of a mark

This is the single richest thresholds category in the whole facts bank: multiple independent series, the identical underlying mechanism (a rounded intermediate value substituted for an exact one), and — uniquely among the categories in this document — one series gives the exact mark-code boundary in the mark scheme's own words.

2.1 The 23.6 / 23.60 cliff — a verbatim mark-scheme threshold

Jan 2021 Q3(b) (same Normal-distribution question as §1's anchor, a different part — "find jj such that P(W>j)=0.15P(W>j)=0.15," 3 marks: M1 correct table selection, then a middle mark, then a final A1). The mark scheme's own precision note, verbatim: "awrt 23.60 scores 3/3 [but] 23.6 scores M1B0A1 unless 1.0364 or better is seen."

2.2 "Ans only" — the opposite threshold, on an ordinary "find" part

Jan 2021 Q3(a) (same question, the first part — "find P(W<10)P(W<10)," 3 marks): the mark scheme credits a bare correct final answer with "Ans only 3/3" for any value in the range 0.0692–0.0694 — full marks, zero working required, provided the final value already carries enough precision to prove it wasn't rounded from something less exact.

2.3 The 4-decimal-place table-value cliff, confirmed independently three times

Unlike §2.1 (one series, one exact mark-scheme quote), this threshold is confirmed by the same mechanism recurring across three separate series, each with its own quoted rounded-vs-exact pair — strong corroboration that this is a stable paper-wide rule, not a one-series quirk:

Series/QJust misses (rounded)Just clears (table-exact)
Jan 2021 Q3(b)1.03 or 1.041.0364
Oct 2021 Q6(b)1.641.6449
Jun 2024 Q5(b)0.25the precise 4-d.p. equivalent

The Jan 2021 examiner report states the mechanism directly: "some students are opting to use calculators for this sort of question and invariably they fail to show sufficient accuracy" — the threshold isn't really about the table specifically, it's that a calculator's own rounded display, or a memorised "nice" value, sits on the wrong side of a line the table's own printed precision defines.

2.4 The sign threshold — same magnitude, wrong side of zero

Jan 2021 Q3(b) (again) and Oct 2021 Q6(b), independently: a candidate reaches the exact right 4-d.p. magnitude and then applies it with the wrong sign — Jan 2021: "others gained this mark but were using −1.0364"; Oct 2021: "using the wrong sign for 1.6449... giving 34.1, a value higher than the upper limit." This is a real, distinct threshold from precision itself: +1.0364 clears the mark that −1.0364 misses, even though both numbers demonstrate the same correct table read-off. Pearson's own stated fix in both reports is identical: draw a diagram first, so the sign is decided by a picture rather than a rule remembered under pressure.


3. Form and simplification thresholds

3.1 The unsimplified-fraction cliff

Jan 2021 Q1(c) (Venn diagram, three events, conditional probability P(A∣B′)P(A\mid B'), mark scheme independently re-verified against the primary PDF for this course's audit of elementary-probability-and-conditional-notation.ts): the M1 line accepts p/0.4p/0.4 for any 0<p<0.40<p<0.4 or the specific working value 0.15/0.40.15/0.4 — but the A1 line requires "=3/8", and the scheme is explicit that an unreduced 0.15/0.40.15/0.4 standing alone does not earn it.

3.2 The fraction-in-a-final-regression-line threshold

Jun 2022 Q2(c) examiner report, verbatim: "it is also important to note that fractions are not accepted in a final regression equation; the values of a and b are both estimates and so a fractional answer is not appropriate." This threshold is unusual among the ones in this document: it is a rule about form, applied irrespective of whether the fraction is even fully simplified — a correct, simplified fraction for aa or bb still misses this specific line, where the identical value written as a decimal clears it. No exact numeric pair for this specific series is quoted in the facts bank beyond the rule itself, so none is invented here — the rule is stated exactly as strongly as the primary source states it, no more precisely.

3.3 A non-threshold, stated for contrast: coding and rr

Jan 2024 MS Q2(d), verbatim: "r not affected by (linear) coding." Worth including here specifically because it is the mirror image of every boundary above: recomputing rr from scratch on the original variables after a coding step, versus reading off the already-computed rr from the coded variables directly, land on the same side of every mark — there is no threshold here to cross, only wasted time in choosing the harder route. Stated explicitly so it isn't mistaken for one.


4. Structural thresholds — where a multi-mark ladder actually breaks

The M/A/B system chains marks together, so the more interesting real thresholds are often not "did you get this one mark" but "how far up a several-mark ladder did you get before something broke." Two full real ladders, independently re-verified in this course's research, are reproduced here completely because nowhere else in the technique-hub gives either one mark-by-mark in full.

4.1 The complete 7-mark ladder — June 2019 Q2(c), an amended box plot

Real question, verbatim task: "Albert's score was changed from 25 to 37. Beth's score was changed from 54 to 60. (c) ... draw an updated box plot. Show clearly any calculations that you used." Original five-number summary (verified from part (a)'s own mark scheme): min 11, Q1=33Q_1=33, median 42, Q3=47Q_3=47, max 54, IQR 14. The full real mark scheme, in order:

RungMarkWhat earns it
1B125→3725\to37 ⇒ new Q1=35Q_1=35
2M1Recognising the new IQR (12) must be recalculated, and that fences must follow
3A1New outlier fences: >47+18=65>47+18=65 or <35−18=17<35-18=17
4M1A box with only two whiskers, median still at 42
5A1ftLower quartile at "their 35" (≠33\ne 33), upper quartile unchanged at 47
6A1Two outliers correctly identified at 11 and 15
7A1Lower whisker at 18 (or 17), upper whisker at 60

The examiner report confirms exactly where real candidates fell off this ladder, and it isn't rung 1: "The major problem was that few candidates realised that the lower quartile would change and increase to 35. Most of those who spotted this realised that this would affect the interquartile range... most others usually just obtained a mark for drawing a box plot with an unchanged median."

4.2 The split 4-mark ladder — June 2024 Q2(c), two independent equations in one part

Real question: Y=aX−bY=aX-b (a,b>0a,b>0), given E(Y)=13.4E(Y)=13.4 and Var(Y)=66.24\mathrm{Var}(Y)=66.24, alongside E(X)=4.6E(X)=4.6 and Var(X)=4.14\mathrm{Var}(X)=4.14 (from an earlier part), "find the value of aa and the value of bb" — 4 marks. Mark scheme, verbatim:

RungMarkWhat earns it
1M1"a² × 4.14 [=66.24]" — the squared-constant variance equation, correctly set up
2A1"a = 4"
3M1"E(Y) =13.4 = a × 4.6 − b" — the separate mean equation, correctly set up
4A1"b = 5"

This ladder is structurally different from §4.1's: it isn't one chain where an early slip cascades, it's two independent two-mark chains bolted into a single question part, and the facts bank's own audit of this lesson found real teaching material (before correction) that closed only the first chain and told the reader the second one "plays no part in it at all" — a genuine, previously-live example of stopping exactly halfway up a ladder that looks, from the first chain alone, like it's already finished.

4.3 "Show that N outliers exist" — the list-them-out completeness threshold

Oct 2021 Q3(c): "having gained the correct limits some did not list the 3 outliers in this part in order to show there are 3 outliers."

4.4 The probability-function domain-sum self-check threshold

Oct 2021 Q4(d): "the most common error was to miss out the value x = 0... had students checked whether the sum of their probabilities equalled 1 they may have realised that they had missed zero out."

4.5 The fixed-vs-shrinking-denominator threshold in sampling without replacement

Jun 2022 Q3(d) (four counters drawn without replacement, "P(all four the same result)" scored on a scheme explicitly acknowledging a named special case): "the most common response was scoring 1 mark for the special case using (62/88)⁴" — keeping the denominator fixed at 88 across all four draws — against the full-marks route that decreases the denominator by one on each successive draw.

4.6 The stop-at-recognition threshold in conditional probability under a Normal model

Jan 2023 Q5(e): "a common error was to find P(L≤5) and go no further" — without dividing by the conditioning event's own probability.

4.7 The E(X)-vs-P(win) threshold — a boundary drawn by which quantity you cite, not by arithmetic

Jun 2019 Q5(e) (two-stage spinner game; E(X)=12E(X)=\tfrac12, P(Amar wins)=716P(\text{Amar wins})=\tfrac{7}{16}, both independently verified elsewhere in the question; the question's own fictional character states "he will play the game" because E(X)>0E(X)>0): mark scheme, verbatim, "[Although E(X) > 0 since] P(win) < 0.5 ... Amar should not play the game or 'disagree'" (M1 A1, 2 marks).


5. Thresholds that run backward — where writing more can cost a mark you'd already earned

Every threshold above rewards showing more work or more precision. This paper also contains the opposite: real, mark-scheme-confirmed cases where the default assumption that extra working is harmless is explicitly switched off.

5.1 The isw override

Default rule, verbatim: "ignore subsequent working" — wrong working after a correct answer normally doesn't cost the mark. Jan 2024 MS Q2(c) switches this off for one specific line: "(do not isw if any further calculation is done after multiplying by 9/5)."

5.2 The box-plot whisker asymmetry — the same mark scheme, two different rules for two whiskers

Jan 2021 Q2(d), verified directly against a rendered image of the mark-scheme page (the facts bank flags pdftotext as unreliable here): the 2nd A1 line reads, verbatim, "for upper whisker ending at 97 and lower whisker ending at 54 or 50 and only one outlier, shown at 43. Allow ± 0.5 of a square for accuracy."


6. What this document deliberately does not contain


Word count and sourcing note for this document specifically: every numeric value, mark code and quotation above is reproduced from research/veridian/WST01-verified-facts.md's own already-verified citations (each traceable there to a named series, question number and, in several cases, a rendered-PDF-page re-check the facts bank records explicitly) or from the corresponding lesson-audit entries in that same file's "Per-lesson bullet-by-bullet coverage audits" section. No new primary source was fetched to write this document; none of its content was generated to hit a target length.