diff --git a/src/__tests__/spread-single-implementation-guard.test.ts b/src/__tests__/spread-single-implementation-guard.test.ts
new file mode 100644
index 000000000..46b5dfa5a
--- /dev/null
+++ b/src/__tests__/spread-single-implementation-guard.test.ts
@@ -0,0 +1,85 @@
+/**
+ * Structural guard: a standard deviation is computed in `lib/stats/spread`,
+ * with its kind named at the call site.
+ *
+ * About a dozen hand-rolled spreads each picked population (÷ n) or sample
+ * (÷ n − 1) without saying so, and the two surfaces a person compares picked
+ * differently: the series API reported the population SD of a blood-pressure
+ * series, the MCP and AI payload the sample SD of the same readings, about
+ * 22 % apart at three readings. The reading spread both report is now
+ * `READING_SPREAD`.
+ *
+ * The matcher flags a squared deviation from a mean in a file that also takes
+ * a square root. The files below compute one for a test statistic or a fit,
+ * never as a reported spread, and say so. The doctor report's glucose panel
+ * composes its SD from per-bucket sums of squares (sample, the same rule as
+ * `glucoseSD`) and is out of the matcher's reach by shape. Comments are
+ * stripped first; the planted case proves the matcher fires.
+ */
+import { readFileSync } from "node:fs";
+import { join } from "node:path";
+import { describe, expect, it } from "vitest";
+
+import { walkSourceFiles } from "./helpers/source-files";
+
+const SRC = join(process.cwd(), "src");
+
+const ALLOWED: Record<string, string> = {
+  "lib/stats/spread.ts": "The implementation.",
+  "lib/insights/correlations.ts":
+    "The correlation engine's centred sums and the Welch t-test variances.",
+  "lib/insights/mood-tag-influence.ts": "Welch t-test variances.",
+  "lib/insights/mood-pattern-cards.ts": "A pooled variance for a t statistic.",
+  "lib/insights/derived/trajectory.ts":
+    "The residual standard error of a regression fit (÷ n − 2).",
+};
+
+const SQUARED_DEVIATION =
+  /\(\s*[\w.[\]]+\s*-\s*[\w.[\]]+\s*\)\s*\*\*\s*2|\(\s*([\w.[\]]+)\s*-\s*([\w.[\]]+)\s*\)\s*\*\s*\(\s*\1\s*-\s*\2\s*\)/;
+
+function stripComments(text: string): string {
+  return text.replace(/\/\*[\s\S]*?\*\//g, "").replace(/^\s*\/\/.*$/gm, "");
+}
+
+function computesSpread(code: string): boolean {
+  return SQUARED_DEVIATION.test(code) && code.includes("Math.sqrt(");
+}
+
+function read(file: string): string {
+  return stripComments(readFileSync(join(SRC, file), "utf8"));
+}
+
+describe("one standard deviation", () => {
+  it("the matcher fires on a hand-rolled spread", () => {
+    expect(
+      computesSpread(
+        "const v = xs.reduce((s, x) => s + (x - m) ** 2, 0) / n; Math.sqrt(v);",
+      ),
+    ).toBe(true);
+    expect(
+      computesSpread("acc += (v - mean) * (v - mean); Math.sqrt(acc / n);"),
+    ).toBe(true);
+  });
+
+  it("no file outside the list computes its own", () => {
+    const offenders = walkSourceFiles(SRC, { floor: 3000 })
+      .filter(
+        (file) =>
+          !file.startsWith("generated/") &&
+          !file.includes("__tests__/") &&
+          !/\.test\.tsx?$/.test(file),
+      )
+      .filter((file) => computesSpread(read(file)) && !(file in ALLOWED));
+    expect(offenders).toEqual([]);
+  });
+
+  it("the series API and the AI and MCP payload report the same spread", () => {
+    expect(read("app/api/measurements/series/route.ts")).toMatch(
+      /standardDeviation\(\s*values,\s*READING_SPREAD\s*\)/,
+    );
+    const features = read("lib/insights/features.ts");
+    expect(
+      features.match(/roundedSpread\(\s*vals,\s*READING_SPREAD\s*\)/g),
+    ).toHaveLength(2);
+  });
+});
diff --git a/src/app/api/measurements/series/route.ts b/src/app/api/measurements/series/route.ts
index b3abf5504..45bb64bb1 100644
--- a/src/app/api/measurements/series/route.ts
+++ b/src/app/api/measurements/series/route.ts
@@ -54,6 +54,7 @@ import {
 import { resolveSeriesReferenceLines } from "@/lib/measurements/series-reference-lines";
 import { getServerTranslator } from "@/lib/i18n/server-translator";
 import { resolveJobLocale } from "@/lib/i18n/job-locale";
+import { READING_SPREAD, standardDeviation } from "@/lib/stats/spread";
 
 /**
  * v1.11.4 — sleep is read row-per-stage (not from the day rollup), so its
@@ -209,10 +210,8 @@ interface SeriesPoint {
 
 function stdDev(values: number[]): number {
   if (values.length < 2) return 0;
-  const mean = values.reduce((sum, v) => sum + v, 0) / values.length;
-  const variance =
-    values.reduce((sum, v) => sum + (v - mean) ** 2, 0) / values.length;
-  return Math.round(Math.sqrt(variance) * 100) / 100;
+  const sd = standardDeviation(values, READING_SPREAD) ?? 0;
+  return Math.round(sd * 100) / 100;
 }
 
 export const GET = apiHandler(async (request: NextRequest) => {
diff --git a/src/lib/analytics/glucose-metrics.ts b/src/lib/analytics/glucose-metrics.ts
index a0f566735..06eca2cee 100644
--- a/src/lib/analytics/glucose-metrics.ts
+++ b/src/lib/analytics/glucose-metrics.ts
@@ -40,6 +40,7 @@
  */
 
 import { GLUCOSE_TIR_CUT_POINTS } from "@/lib/glucose";
+import { standardDeviation } from "@/lib/stats/spread";
 
 // ── Inputs ───────────────────────────────────────────────
 
@@ -236,15 +237,7 @@ function mean(values: number[]): number {
  * Returns null for n < 2 (undefined sample SD).
  */
 export function glucoseSD(values: number[]): number | null {
-  const n = values.length;
-  if (n < 2) return null;
-  const m = mean(values);
-  let ss = 0;
-  for (const v of values) {
-    const d = v - m;
-    ss += d * d;
-  }
-  return Math.sqrt(ss / (n - 1));
+  return standardDeviation(values, "sample");
 }
 
 /**
diff --git a/src/lib/analytics/mood-prognosis/features.ts b/src/lib/analytics/mood-prognosis/features.ts
index 467b71236..53f012998 100644
--- a/src/lib/analytics/mood-prognosis/features.ts
+++ b/src/lib/analytics/mood-prognosis/features.ts
@@ -68,6 +68,7 @@ import {
   LINKED_FEATURE_METRICS,
 } from "./feature-keys";
 import { occurrencesSuffice } from "./thresholds";
+import { standardDeviation } from "@/lib/stats/spread";
 
 /**
  * Most features the fit may carry.
@@ -444,10 +445,7 @@ export function buildFeatureMatrix(
   const standardisation = selected.map((key, column) => {
     const values = rawRows.map((row) => row[column]);
     const mean = values.reduce((sum, v) => sum + v, 0) / values.length;
-    const variance =
-      values.reduce((sum, v) => sum + (v - mean) * (v - mean), 0) /
-      values.length;
-    return { key, mean, sd: Math.sqrt(variance) };
+    return { key, mean, sd: standardDeviation(values, "population") ?? 0 };
   });
 
   // A column with no spread inside the complete-case set carries no
diff --git a/src/lib/analytics/score/activity.ts b/src/lib/analytics/score/activity.ts
index 4601eb786..326363dfd 100644
--- a/src/lib/analytics/score/activity.ts
+++ b/src/lib/analytics/score/activity.ts
@@ -9,7 +9,7 @@ import {
   insufficientPillar,
   mean,
   okPillar,
-  standardDeviation,
+  readingSpread,
 } from "./shared";
 
 export const ACTIVITY_WINDOW_DAYS = 28;
@@ -74,7 +74,7 @@ export function computeActivityPillar(
   const score = clampScore((observed / plateau) * 100);
   const noiseFloor = Math.max(
     1,
-    Math.round(((0.5 * standardDeviation(values)) / plateau) * 100),
+    Math.round(((0.5 * readingSpread(values)) / plateau) * 100),
   );
   const latestDay = [...points].sort((a, b) => b.day.localeCompare(a.day))[0];
 
diff --git a/src/lib/analytics/score/glycaemia.ts b/src/lib/analytics/score/glycaemia.ts
index b62462a02..dca0bb893 100644
--- a/src/lib/analytics/score/glycaemia.ts
+++ b/src/lib/analytics/score/glycaemia.ts
@@ -10,7 +10,7 @@ import {
   median,
   okPillar,
   scoreReferenceBand,
-  standardDeviation,
+  readingSpread,
   uniqueSources,
   withinWindow,
 } from "./shared";
@@ -126,7 +126,7 @@ export function computeGlycaemiaPillar(
   const observed = median(values);
   // The behavioural/device noise convention from the design is one half of
   // within-person SD, translated onto this pillar's proportional score scale.
-  const halfSd = standardDeviation(values) * 0.5;
+  const halfSd = readingSpread(values) * 0.5;
   const floorScore = scoreReferenceBand(
     Math.max(0, observed - halfSd),
     FASTING_GLUCOSE_REFERENCE.low,
diff --git a/src/lib/analytics/score/shared.ts b/src/lib/analytics/score/shared.ts
index e5dfbbdfa..1fa3bff2d 100644
--- a/src/lib/analytics/score/shared.ts
+++ b/src/lib/analytics/score/shared.ts
@@ -11,6 +11,7 @@ import type {
 } from "@/lib/insights/derived/types";
 
 import type { PillarValue, ScoreBand, ScorePillarId } from "./types";
+import { READING_SPREAD, standardDeviation } from "@/lib/stats/spread";
 
 export const DAY_MS = 86_400_000;
 
@@ -88,11 +89,9 @@ export function median(values: readonly number[]): number {
     : ordered[middle];
 }
 
-export function standardDeviation(values: readonly number[]): number {
+export function readingSpread(values: readonly number[]): number {
   if (values.length < 2) return 0;
-  const center = mean(values);
-  const variance = mean(values.map((value) => (value - center) ** 2));
-  return Math.sqrt(variance);
+  return standardDeviation(values, READING_SPREAD) ?? 0;
 }
 
 export function uniqueSources(values: readonly string[]): string[] {
diff --git a/src/lib/analytics/score/sleep.ts b/src/lib/analytics/score/sleep.ts
index 086fd887c..bebc81462 100644
--- a/src/lib/analytics/score/sleep.ts
+++ b/src/lib/analytics/score/sleep.ts
@@ -13,7 +13,7 @@ import {
   insufficientPillar,
   mean,
   okPillar,
-  standardDeviation,
+  readingSpread,
 } from "./shared";
 
 export const SLEEP_WINDOW_DAYS = 28;
@@ -75,7 +75,7 @@ export function computeSleepPillar(
       : Math.round(sufficiency * 0.6 + regularity * 0.4);
   const noiseFloor = Math.max(
     1,
-    Math.round(((0.5 * standardDeviation(asleepValues)) / need) * 100),
+    Math.round(((0.5 * readingSpread(asleepValues)) / need) * 100),
   );
   const latest = nights.at(-1)!;
 
diff --git a/src/lib/analytics/trends.ts b/src/lib/analytics/trends.ts
index 242f30bea..08b17d4d7 100644
--- a/src/lib/analytics/trends.ts
+++ b/src/lib/analytics/trends.ts
@@ -3,6 +3,8 @@
  * All functions are pure and work on sorted arrays of {date, value} pairs.
  */
 
+import { READING_SPREAD, standardDeviation } from "@/lib/stats/spread";
+
 export interface DataPoint {
   date: Date;
   value: number;
@@ -95,9 +97,7 @@ export function detectAnomalies(data: DataPoint[], threshold = 2.0): Anomaly[] {
 
   const values = data.map((p) => p.value);
   const mean = values.reduce((s, v) => s + v, 0) / values.length;
-  const variance =
-    values.reduce((s, v) => s + (v - mean) ** 2, 0) / values.length;
-  const stdDev = Math.sqrt(variance);
+  const stdDev = standardDeviation(values, READING_SPREAD) ?? 0;
 
   if (stdDev === 0) return [];
 
diff --git a/src/lib/insights/__tests__/features.test.ts b/src/lib/insights/__tests__/features.test.ts
index f43d56adf..0f582b50c 100644
--- a/src/lib/insights/__tests__/features.test.ts
+++ b/src/lib/insights/__tests__/features.test.ts
@@ -682,3 +682,24 @@ describe("extractFeatures — a day of pulse is the mean of its hours' means", (
     expect(f.historicalComparison?.pulse?.current7dAvg).toBe(71.25);
   });
 });
+
+describe("extractFeatures — blood-pressure spread", () => {
+  it("reports the same population spread the series API shows", async () => {
+    // 120 / 130 / 140 over the last three days: population SD 8.165, the
+    // sample SD (the old rule here) would be 10.
+    const day = 24 * 60 * 60 * 1000;
+    const rows = [120, 130, 140].map((value, i) => ({
+      type: "BLOOD_PRESSURE_SYS",
+      value,
+      measuredAt: new Date(Date.now() - (i + 1) * day),
+      sleepStage: null,
+      source: "MANUAL",
+      deviceType: null,
+    }));
+    prismaMock.measurement.findMany.mockResolvedValue(rows);
+
+    const features = await extractFeatures("user-1", false);
+
+    expect(features.bloodPressure?.sdSys30).toBe(8.2);
+  });
+});
diff --git a/src/lib/insights/features.ts b/src/lib/insights/features.ts
index cc24519de..ee6c70f76 100644
--- a/src/lib/insights/features.ts
+++ b/src/lib/insights/features.ts
@@ -30,6 +30,11 @@ import {
 import { loadUserSourcePriority } from "@/lib/rollups/measurement-read";
 import { getBpTargets } from "@/lib/analytics/bp-targets";
 import { isBpReadingInTarget } from "@/lib/analytics/bp-in-target";
+import {
+  READING_SPREAD,
+  standardDeviation,
+  type VarianceKind,
+} from "@/lib/stats/spread";
 import {
   pairByTimestamp,
   significantPearsonCorrelation,
@@ -894,12 +899,17 @@ export class FeaturesPayloadTooLargeError extends Error {
   }
 }
 
-export function stdDev(values: number[]): number | null {
+/**
+ * A spread rounded to the payload's one decimal, `null` below two values: a
+ * single reading has no spread to report, not a spread of zero.
+ */
+export function roundedSpread(
+  values: readonly number[],
+  kind: VarianceKind,
+): number | null {
   if (values.length < 2) return null;
-  const mean = values.reduce((s, v) => s + v, 0) / values.length;
-  const variance =
-    values.reduce((s, v) => s + (v - mean) ** 2, 0) / (values.length - 1);
-  return Math.round(Math.sqrt(variance) * 10) / 10;
+  const sd = standardDeviation(values, kind);
+  return sd === null ? null : Math.round(sd * 10) / 10;
 }
 
 export function toDataPoints(
@@ -1468,14 +1478,14 @@ export async function extractFeatures(
         const vals = sysData
           .filter((m) => m.measuredAt.getTime() >= fromMs)
           .map((m) => m.value);
-        return stdDev(vals);
+        return roundedSpread(vals, READING_SPREAD);
       })(),
       sdDia30: (() => {
         const fromMs = now - 30 * 24 * 60 * 60 * 1000;
         const vals = diaData
           .filter((m) => m.measuredAt.getTime() >= fromMs)
           .map((m) => m.value);
-        return stdDev(vals);
+        return roundedSpread(vals, READING_SPREAD);
       })(),
       pulsePressure30: (() => {
         const avgSys = sysSummary?.avg30 ?? null;
diff --git a/src/lib/insights/metric-signal.ts b/src/lib/insights/metric-signal.ts
index 1dbf261fd..8f943b256 100644
--- a/src/lib/insights/metric-signal.ts
+++ b/src/lib/insights/metric-signal.ts
@@ -25,6 +25,7 @@
  */
 import type { GradedSeries } from "@/lib/insights/graded-series";
 import type { NormRange } from "@/lib/insights/derived/norms";
+import { standardDeviation } from "@/lib/stats/spread";
 
 /** Favourable-direction framing — mirrors the metric-status registry. */
 export type MetricDirection = "higher-better" | "lower-better" | "target-band";
@@ -96,16 +97,6 @@ function meanOf(values: number[]): number | null {
   return sum / values.length;
 }
 
-/** Sample standard deviation, or null with fewer than two points. */
-function sampleSd(values: number[]): number | null {
-  if (values.length < 2) return null;
-  const m = meanOf(values);
-  if (m === null) return null;
-  let acc = 0;
-  for (const v of values) acc += (v - m) ** 2;
-  return Math.sqrt(acc / (values.length - 1));
-}
-
 /** Placement of a value against a coarse normal range. */
 export function placeInBand(
   value: number,
@@ -169,7 +160,8 @@ export function buildMetricSignal(
   }
 
   const baseline = meanOf(baselineMeans);
-  const spread = sampleSd(baselineMeans);
+  // The spread decides the verdict, so it is the sample estimate.
+  const spread = standardDeviation(baselineMeans, "sample");
 
   let delta: number | null = null;
   let deltaPct: number | null = null;
diff --git a/src/lib/insights/mood-patterns.ts b/src/lib/insights/mood-patterns.ts
index 7dc5fb218..289748095 100644
--- a/src/lib/insights/mood-patterns.ts
+++ b/src/lib/insights/mood-patterns.ts
@@ -20,6 +20,7 @@ import {
 import { round } from "@/lib/insights/status-shared";
 import { DEFAULT_TIMEZONE } from "@/lib/tz/format";
 import { wallClockInTz } from "@/lib/tz/wall-clock";
+import { READING_SPREAD, standardDeviation } from "@/lib/stats/spread";
 
 // --- In-target % over the last 30 daily points (lifted from mood-status) ---
 
@@ -289,11 +290,11 @@ export function computeMoodStability(
 ): MoodStability | null {
   if (daily.length < STABILITY_MIN_DAYS) return null;
 
-  const values = daily.map((bucket) => bucket.value);
-  const avg = values.reduce((sum, v) => sum + v, 0) / values.length;
-  const variance =
-    values.reduce((sum, v) => sum + (v - avg) ** 2, 0) / values.length;
-  const stdDev = Math.sqrt(variance);
+  const stdDev =
+    standardDeviation(
+      daily.map((bucket) => bucket.value),
+      READING_SPREAD,
+    ) ?? 0;
 
   const normalised =
     Math.min(stdDev, STABILITY_SD_FULL_SCALE) / STABILITY_SD_FULL_SCALE;
diff --git a/src/lib/insights/seasonal-adjust.ts b/src/lib/insights/seasonal-adjust.ts
index 4db5e1c67..5be724265 100644
--- a/src/lib/insights/seasonal-adjust.ts
+++ b/src/lib/insights/seasonal-adjust.ts
@@ -29,6 +29,8 @@
  * the regression runs over the days that exist and nothing is imputed.
  */
 
+import { variance as varianceOf } from "@/lib/stats/spread";
+
 /** Span (first to last paired day, inclusive) below which only the trend is removed. */
 export const SEASONAL_MIN_SPAN_DAYS = 120;
 
@@ -205,10 +207,11 @@ function densify(
     dense[days[i] - lo] = values[i];
     sum += values[i];
   }
-  const mean = sum / values.length;
-  let ss = 0;
-  for (const v of values) ss += (v - mean) ** 2;
-  return { dense, mean, variance: ss / values.length };
+  return {
+    dense,
+    mean: sum / values.length,
+    variance: varianceOf(values, "population") ?? 0,
+  };
 }
 
 /**
diff --git a/src/lib/insights/signals-of-day.ts b/src/lib/insights/signals-of-day.ts
index b522db563..3be2c7e0c 100644
--- a/src/lib/insights/signals-of-day.ts
+++ b/src/lib/insights/signals-of-day.ts
@@ -9,7 +9,11 @@
  * so every existing call site keeps importing from there.
  */
 import { trendSlope } from "@/lib/analytics/trends";
-import { avgInWindow, stdDev, toDataPoints } from "@/lib/insights/features";
+import {
+  avgInWindow,
+  roundedSpread,
+  toDataPoints,
+} from "@/lib/insights/features";
 import {
   SAME_HOURS_MIN_DAYS,
   SAME_HOURS_TYPES,
@@ -177,7 +181,11 @@ function buildSignal(
   // spread and the anomaly stay over the readings.
   const avg7 = avgInWindow(records, now, 7, 0, day);
   const avg30 = avgInWindow(records, now, 30, 0, day);
-  const spread30 = stdDev(win30.map((rec) => rec.value));
+  // The spread decides the verdict below, so it is the sample estimate.
+  const spread30 = roundedSpread(
+    win30.map((rec) => rec.value),
+    "sample",
+  );
   const deltaVs7 = avg7 !== null ? shown(newest.value - avg7) : null;
   const deltaVs30 = avg30 !== null ? shown(newest.value - avg30) : null;
   const outsideNormalSwing =
@@ -310,7 +318,10 @@ function buildSameHoursSignal(
 
   const avg30 = mean(earlier.map((d) => d.value));
   const avg7 = mean(earlier.filter((d) => d.age <= 7).map((d) => d.value));
-  const spread30 = stdDev(earlier.map((d) => d.value));
+  const spread30 = roundedSpread(
+    earlier.map((d) => d.value),
+    "sample",
+  );
   const latest = today.value;
   const outsideNormalSwing =
     avg30 !== null && spread30 !== null && spread30 > 0
diff --git a/src/lib/mcp/rich-reads.ts b/src/lib/mcp/rich-reads.ts
index 4c7318286..53329ae9e 100644
--- a/src/lib/mcp/rich-reads.ts
+++ b/src/lib/mcp/rich-reads.ts
@@ -63,6 +63,7 @@ import { sanitizeValueText } from "@/lib/ai/coach/labs-snapshot";
 import { scrubFenceMarkers } from "@/lib/ai/coach/data-fence";
 import { encodeOffsetCursor } from "@/lib/mcp/pagination";
 import type { CoachScopeWindow } from "@/lib/ai/coach/types";
+import { standardDeviation } from "@/lib/stats/spread";
 
 const DAY_MS = 24 * 60 * 60 * 1000;
 
@@ -1158,11 +1159,9 @@ function mean(xs: number[]): number {
   return xs.reduce((s, x) => s + x, 0) / xs.length;
 }
 
+/** The CUSUM threshold estimates the series' noise, so it is the sample SD. */
 function stdDev(xs: number[]): number {
-  if (xs.length < 2) return 0;
-  const m = mean(xs);
-  const variance = xs.reduce((s, x) => s + (x - m) ** 2, 0) / (xs.length - 1);
-  return Math.sqrt(variance);
+  return standardDeviation(xs, "sample") ?? 0;
 }
 
 /**
diff --git a/src/lib/rollups/tiered-context.ts b/src/lib/rollups/tiered-context.ts
index b73f6073d..931911e5b 100644
--- a/src/lib/rollups/tiered-context.ts
+++ b/src/lib/rollups/tiered-context.ts
@@ -43,6 +43,7 @@ import { readDayAggregates } from "@/lib/measurements/day-aggregates";
 import { dayWeightedRowsSql, windowMeanSql } from "@/lib/measurements/day-mean";
 import { usesHourlyMeanDay } from "@/lib/measurements/day-statistic";
 import { Prisma } from "@/generated/prisma/client";
+import { READING_SPREAD, standardDeviation } from "@/lib/stats/spread";
 
 const DAY_MS = 24 * 60 * 60 * 1000;
 
@@ -203,9 +204,8 @@ function windowStats(buckets: RollupBucket[]): {
   const means = usable.map((b) => b.mean);
   const mean = means.reduce((s, m) => s + m, 0) / means.length;
   if (means.length < 2) return { mean: round(mean), sd: null, n };
-  const variance =
-    means.reduce((s, m) => s + (m - mean) ** 2, 0) / means.length;
-  return { mean: round(mean), sd: round(Math.sqrt(variance)), n };
+  const sd = standardDeviation(means, READING_SPREAD) ?? 0;
+  return { mean: round(mean), sd: round(sd), n };
 }
 
 /**
diff --git a/src/lib/stats/__tests__/spread.test.ts b/src/lib/stats/__tests__/spread.test.ts
new file mode 100644
index 000000000..5192b17f7
--- /dev/null
+++ b/src/lib/stats/__tests__/spread.test.ts
@@ -0,0 +1,23 @@
+import { describe, expect, it } from "vitest";
+
+import { READING_SPREAD, standardDeviation, variance } from "../spread";
+
+describe("spread", () => {
+  const values = [120, 130, 140];
+
+  it("divides by n for a population and by n - 1 for a sample", () => {
+    expect(variance(values, "population")).toBeCloseTo(200 / 3, 10);
+    expect(variance(values, "sample")).toBe(100);
+    expect(standardDeviation(values, "sample")).toBe(10);
+  });
+
+  it("is undefined below what the kind needs", () => {
+    expect(variance([], "population")).toBeNull();
+    expect(variance([5], "population")).toBe(0);
+    expect(variance([5], "sample")).toBeNull();
+  });
+
+  it("reports readings as a population", () => {
+    expect(READING_SPREAD).toBe("population");
+  });
+});
diff --git a/src/lib/stats/spread.ts b/src/lib/stats/spread.ts
new file mode 100644
index 000000000..c06c944c5
--- /dev/null
+++ b/src/lib/stats/spread.ts
@@ -0,0 +1,49 @@
+/**
+ * Variance and standard deviation, with the kind named at every call site.
+ *
+ * - `population` divides by n: the spread of exactly these readings. It is
+ *   what a surface reports when it describes a series the person can see.
+ * - `sample` divides by n − 1: an estimate of the spread that readings like
+ *   these come from. It belongs where the spread feeds a decision (a
+ *   significance verdict, a changepoint threshold) or where a clinical
+ *   definition asks for it.
+ *
+ * The two differ by sqrt(n / (n − 1)), about 22 % at n = 3, so one series
+ * shown with both rules looks like two different series. Every hand-rolled
+ * spread used to pick its rule silently; the API reported the population SD
+ * of a blood-pressure series while the MCP and AI payload reported the
+ * sample SD of the same readings.
+ */
+
+export type VarianceKind = "population" | "sample";
+
+/**
+ * The kind every surface uses to report the spread of a person's readings,
+ * so the API, the MCP tools, the Coach and the AI payload say the same
+ * number for the same series.
+ */
+export const READING_SPREAD: VarianceKind = "population";
+
+/** `null` when the kind is undefined for this many values (n < 1, or n < 2 for a sample). */
+export function variance(
+  values: readonly number[],
+  kind: VarianceKind,
+): number | null {
+  const n = values.length;
+  const divisor = kind === "sample" ? n - 1 : n;
+  if (divisor < 1) return null;
+  let sum = 0;
+  for (const v of values) sum += v;
+  const mean = sum / n;
+  let squares = 0;
+  for (const v of values) squares += (v - mean) ** 2;
+  return squares / divisor;
+}
+
+export function standardDeviation(
+  values: readonly number[],
+  kind: VarianceKind,
+): number | null {
+  const v = variance(values, kind);
+  return v === null ? null : Math.sqrt(v);
+}
diff --git a/src/lib/targets/mood-builder.ts b/src/lib/targets/mood-builder.ts
index 2e48e76c7..fdb917ae7 100644
--- a/src/lib/targets/mood-builder.ts
+++ b/src/lib/targets/mood-builder.ts
@@ -5,6 +5,7 @@ import type {
   TargetMoodRollup,
   TargetTrend,
 } from "./types";
+import { READING_SPREAD, standardDeviation } from "@/lib/stats/spread";
 
 interface MoodTargetInput {
   moodRollups: TargetMoodRollup[];
@@ -24,9 +25,6 @@ export function buildMoodTargets({
   const thirtyDaysAgo = new Date(now.getTime() - 30 * 24 * 60 * 60 * 1000);
   let dailyEvents: Array<{ measuredAt: Date; value: number }>;
   let entryCount: number;
-  let sumScores: number;
-  let varianceCount: number;
-  let sumSquares: number;
 
   if (moodRollups.length > 0) {
     entryCount = moodRollups.reduce((sum, rollup) => sum + rollup.count, 0);
@@ -36,12 +34,6 @@ export function buildMoodTargets({
         measuredAt: rollup.bucketStart,
         value: rollup.mean,
       }));
-    sumScores = dailyEvents.reduce((sum, event) => sum + event.value, 0);
-    varianceCount = dailyEvents.length;
-    sumSquares = dailyEvents.reduce(
-      (sum, event) => sum + event.value * event.value,
-      0,
-    );
   } else if (latestMoodEntry !== null) {
     const rawMood = recentRawMood ?? [];
     entryCount = rawMood.length;
@@ -49,26 +41,20 @@ export function buildMoodTargets({
       measuredAt: entry.moodLoggedAt,
       value: entry.score,
     }));
-    sumScores = rawMood.reduce((sum, entry) => sum + entry.score, 0);
-    varianceCount = rawMood.length;
-    sumSquares = rawMood.reduce(
-      (sum, entry) => sum + entry.score * entry.score,
-      0,
-    );
   } else {
     entryCount = 0;
     dailyEvents = [];
-    sumScores = 0;
-    varianceCount = 0;
-    sumSquares = 0;
   }
+  const values = dailyEvents.map((event) => event.value);
 
   if (entryCount < 3) return [];
 
   const current = latestMoodEntry?.score ?? null;
   const average30 =
-    dailyEvents.length > 0
-      ? Math.round((sumScores / dailyEvents.length) * 10) / 10
+    values.length > 0
+      ? Math.round(
+          (values.reduce((sum, v) => sum + v, 0) / values.length) * 10,
+        ) / 10
       : null;
   let trend: TargetTrend = null;
   if (dailyEvents.length >= 4) {
@@ -118,23 +104,21 @@ export function buildMoodTargets({
     },
   ];
 
-  if (varianceCount >= 5) {
-    const mean = sumScores / varianceCount;
-    const variance = sumSquares / varianceCount - mean * mean;
-    const standardDeviation =
-      Math.round(Math.sqrt(Math.max(0, variance)) * 100) / 100;
+  if (values.length >= 5) {
+    const spread =
+      Math.round((standardDeviation(values, READING_SPREAD) ?? 0) * 100) / 100;
     targets.push({
       type: "MOOD_STABILITY",
       label: "Mood stability",
-      current: standardDeviation,
-      average30: standardDeviation,
+      current: spread,
+      average30: spread,
       trend: null,
       unit: "σ",
       range: { min: 0, max: 0.5 },
       classification:
-        standardDeviation <= 0.5
+        spread <= 0.5
           ? { category: "Very stable", color: "var(--success)" }
-          : standardDeviation <= 1
+          : spread <= 1
             ? { category: "Stable", color: "var(--dracula-yellow)" }
             : { category: "Fluctuating", color: "var(--destructive)" },
       source: "Mood entries",