Topic Brief: Measures of Location and Dispersion

#SIGNAL Topic Master Brief — Measures of Location and Dispersion (WST01, spec 2.2/2.3)

Provenance (2026-09-29): built from research/veridian/WST01-verified-facts.md (compiled 2026-09-12, spot-check addendum 2026-09-25), grepped for "mean", "median", "coding", "standard deviation", "variance", "interpolat", "quartile" and "IQR", and cross-checked against codex-deep-dive-measures-of-location-and-dispersion.md and signal-frequency-and-boundaries.md (both in this folder) so this document does not restate either. CODEX already carries the full formal derivations, the sub-case worked examples, and a per-question synthesis table; the frequency doc already gives the whole-Section-2 (spec 2.1–2.4 combined) "6 of 6" figure. This document adds three things neither of those states as its own subject: the narrowed frequency count for this lesson's own 2.2/2.3 core specifically, the mark-tariff and paper-position pattern across the confirmed series, and an explicit note on which angle types recur versus which appear once each — none of that cross-series aggregation exists elsewhere in this folder. No new PDF fetches were made. Every claim below cites a series and question from the facts bank.

#1. Frequency — seen in 4 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. Narrowed to this lesson's own core — mean, coding, standard deviation, and interpolation for quartiles/percentiles (spec 2.2/2.3, not the histogram-reading or outlier/box-plot content of 2.1/2.4) — a distinct, cited exam angle is confirmed in 4 of those 6: Jan 2021, Oct 2021, Jun 2022, Jan 2023. Jun 2024's only Section-2 citation is a stem-and-leaf misread that swapped Q1/Q3 (spec 2.1, a reading error, not a 2.2/2.3 calculation), and the Jun 2019 spot-check surfaced nothing new specific to this core. This is a narrower count than the "6 of 6" row in signal-frequency-and-boundaries.md, which pools all four Section-2 sub-points together — the two figures answer different questions and should not be read as the same claim.

Worth stating plainly: this core is not among the topics §7 of the facts bank lists as having "enough verified material for a genuine standalone lesson" (that list names outliers/box plots, conditional probability, sampling, regression wording, E(aX+b)/Var(aX+b), and the Normal distribution — not this one). The evidence is real and cited, but narrower and more concentrated than several other WST01 topics — mostly one dense multi-part question plus a handful of single-series citations, not a wide spread of independently-varied examples.

#2. What was actually tested, and which angles repeat versus appear once

• Jan 2023 Q1(c)–(e), one grouped frequency table (swim times, n=100), three sub-skills in sequence. (c) mean from the table — ER: "some added the frequencies and divided by 5 [the number of classes] whilst others used the sum of class width multiplied by the frequencies." (d) the standard deviation, with the ER quoting two distinct malformed formula shapes and the mark scheme separately crediting a /n and a /(n−1) route for the same 2 marks. (e) interpolation for a quartile — ER: "those that worked with n rather than n+1 were usually more successful."
• Jun 2022 Q3(e), coding (log-length data, y=(x−255)/2). Mean-decoding mostly succeeded, but ER: "correct answers for variance of W were much rarer, with candidates not decoding, commonly including the assumed mean of 255, scaling using 0.5 instead of 0.5², or knowing they should use 0.5² but multiplying instead of dividing."
• Jan 2021 Q6(c), combining two groups' data. ER: candidates "forgot to square the standard deviation of 2 when finding Σy² for the second group" — recovering a sum-of-squares from a given mean and SD.
• Oct 2021 Q3(b), a "show that [IQR] = 16" question. ER: "the main errors, since the answer was given, were making up two ages... which differed by 16 as their 'working'" — i.e. reverse- engineering the given answer instead of interpolating genuinely.

Setting these four side by side shows something neither existing document states. First, the squaring step in variance/SD arithmetic is the one thread that repeats across series, not just within one: Jan 2021 Q6(c) and Jan 2023 Q1(d) are two years apart and different question shapes (recovering Σy² backward vs building the SD forward), yet both fail at the identical step — a constant or total that should be squared once, isn't, or is squared then mishandled. Jun 2022 Q3(e)'s "0.5 instead of 0.5²" is the same species again, inside coding. Second, the mean-from-a-table denominator slip and the interpolation "show that" fabrication are each confirmed only once (Jan 2023 Q1(c); Oct 2021 Q3(b)) — real and citable, but not yet independently repeated like the squaring error.

#3. Mark-tariff and paper-position pattern

Only one series in the facts bank carries an explicit, quoted mark-by-mark breakdown for this core: Jan 2023 Q1(d), scored M1 (for Σft²) then M1 A1 for the SD itself — 3 marks, with the M1A1 pair crediting either arithmetic route. No other series' exact mark allocation for this specific sub-skill is quoted in the source, and this document does not estimate one.

Position in the paper varies rather than repeating a slot: this content has opened the paper as Q1 (Jan 2023), sat mid-paper as Q3 (Oct 2021, Jun 2022), and appeared as late as Q6 (Jan 2021). Do not coach a fixed expectation of where in the paper it lands.

#4. Recurring context/angle across the confirmed series

The one structural pattern that is genuinely repeatable: when this content is examined at any length, it tends to arrive as a multi-part sequence built on a single grouped frequency table (mean, then SD, then an interpolated statistic, all off the same dataset) rather than as isolated, unrelated questions — Jan 2023 Q1 is the clearest confirmed instance of that shape. Coding, by contrast, has so far appeared as its own separate scenario (Jun 2022) rather than layered onto the same multi-part table. The "show that [a given interpolated value]" framing is a specific, named instance of the paper-wide "show that" discipline problem Pearson itself flags as its single most repeated general complaint (see this folder's forge guide) — it is not unique to this topic, but it does concretely recur here (Oct 2021 Q3(b)).

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

Expect it most often as part of a multi-part grouped-table question — mean, SD and an interpolated quartile or percentile off the same data are a confirmed real shape, not a hypothetical one. Whatever the specific calculation, check the squaring step first: a coding constant squared for variance but not for the mean, a given SD squared to recover Σy², or a raw total squared and divided by n only once instead of twice — this is the one error that has independently recurred across more than one series. If a value is "given" and the question asks you to show it (an IQR, a percentile), the credited method is genuine interpolation with every step shown, not two invented numbers with the right gap between them. No fixed mark value or paper position is safe to assume; this content has carried as few as 2–3 clearly-quoted marks in one part and has appeared anywhere from Q1 to Q6 across the confirmed series.

#Sources and limitations

All citations trace to research/veridian/WST01-verified-facts.md §5 (Section 2) and its dedicated per-lesson audit entry for measures-of-location-and-dispersion.ts. Frequency is stated only as "N of 6 series checked" — no percentage or likelihood claim is made anywhere in this document, and no grade-boundary figure is used (none exists in the source material; see signal-frequency-and- boundaries.md §2). The 8 series without a located examiner report (Jun 2021, Jan 2022, Oct 2022, Jun 2023, Oct 2023, Jan 2024, Oct 2024, Jan 2025) were not searched for this topic and are excluded from both the numerator and denominator above. This document does not repeat the formal derivations, sub-case worked examples, or per-question synthesis table already in codex-deep-dive-measures-of- location-and-dispersion.md, nor the whole-Section-2 frequency row in signal-frequency-and- boundaries.md.