Statistics Notes — Gap Audit (28 Aug 2026, SUPERSEDED)
This was the audit of Notes-Statistics.md as it stood on 28 August 2026. Every gap it reports below has since been filled inside the notes themselves. It is kept only as a record of what was found and why.
| This file says | Status now |
|---|---|
| 🔴 GAP 1 — Probability completely absent | ✅ Written in full as TOPIC (vi) — THEORY OF PROBABILITY (9 sections, 4 worked examples, trap table) |
| 🟠 GAP 2 — Sampling error missing | ✅ Added in Topic (ii) |
| 🟠 GAP 3 — Empirical relation missing | ✅ Added as Topic (v), 5.1 |
| 🟠 GAP 4 — Census 2011 facts / Nagaland | ✅ Added as Topic (ix), 6.1 |
| 🟡 GAP 5 — Polygon → curve limit | ✅ Added in Topic (iv), 7.5 |
| 🟡 GAP 6 — Time series / moving average | ✅ PYQ marker added at Topic (iv), 4.1 |
| 📊 Scorecard: "Cannot answer 4" | ❌ No longer true — those four are now covered |
The scorecard at the bottom is the most misleading part. It was ~10–13 of 17 when written; after the gap-fills it is ~16–17 of 17.
⚠️ Two corrections were flagged but deliberately not rewritten in the author's body text (they sit as [!fix] callouts beside the original): the sex ratio 940 → 943 and the "Simultaneity" definition.
👉 Current, live files: Notes-Statistics · Statistics-Study-Plan · Statistics-Tagged-Answers · Statistics-Analysis-and-Mapping
📌 ADDENDUM — gap-fill & accuracy audit (added 28 Aug 2026)
Audited against all 20 statistics questions from the 2022 and 2024 FAA papers — see Statistics-Tagged-Answers. Verdict: 9 of the 10 syllabus topics are covered excellently. One topic is missing entirely.
🔴 GAP 1 — THEORY OF PROBABILITY IS COMPLETELY ABSENT
Syllabus topic (vi). The word "probability" does not appear once in these notes. It was asked in BOTH papers — 2024·Q76 and 2022·Q34 — and since the 2024 paper asked exactly one question per syllabus topic, this is a guaranteed 1 mark you cannot currently answer.
The minimum you need
0 ≤ P(A) ≤ 1 · impossible event = 0 · certain event = 1 · P(A) + P(Ā) = 1 P(A) = favourable outcomes ÷ total outcomes
| Rule | Formula |
|---|---|
| Addition (general) | P(A∪B) = P(A) + P(B) − P(A∩B) |
| Mutually exclusive | P(A∩B) = 0 → P(A∪B) = P(A) + P(B) |
| Multiplication (independent) | P(A∩B) = P(A) × P(B) |
| Conditional | P(A|B) = P(A∩B) ÷ P(B) |
Key terms: exhaustive (covers all outcomes) · mutually exclusive (cannot occur together) · independent (one does not affect the other).
- Mutually exclusive events sum to 1 ONLY IF they are also exhaustive. Being mutually exclusive alone is not enough (2024·Q76).
- "Probability can never be zero" is FALSE — an impossible event has probability exactly 0.
- ⭐ Any option greater than 1 cannot be a probability. In 2022·Q34 that eliminated three of the four options instantly.
Worked example (2022·Q34 type): P(Maths) = 2/5, P(Physics) = 3/10, P(both) = 1/5. P(M∪P) = 2/5 + 3/10 − 1/5 = 4/10 + 3/10 − 2/10 = 5/10 = 1/2 ✓
🟠 GAP 2 — Sampling error (topic ii)
2022·Q31 asked exactly this. Not covered above.
- ⭐ Sampling error DECREASES as sample size INCREASES
- A census (complete enumeration) has NO sampling error — but may still have non-sampling errors
- Non-sampling errors (measurement, coverage, response, processing) can occur in both censuses and samples, and may rise with sample size
🟠 GAP 3 — Empirical relation (topic v) — flagged inline above
⭐ Mode = 3 Median − 2 Mean
🟠 GAP 4 — Census 2011 standout facts (topic ix) — flagged inline above
⭐ Sex ratio = 943 (not 940) · ⭐ Nagaland = only state with negative decadal growth (−0.58%) Also memorise: population 121.09 crore · decadal growth 17.7% · density 382/km² · literacy 74.04%
🟡 GAP 5 — Frequency polygon → curve (topic iv)
2022·Q38 asked what happens to a frequency polygon as the number of classes increases. ⭐ It becomes increasingly SMOOTH — in the limit, the polygon becomes a frequency curve. The notes define the frequency curve but never state this limiting relationship.
🟡 GAP 6 — Time series / moving averages (off the 10 topics)
2022·Q33 asked a 3-month moving average. This is NOT in the FAA statistics syllabus (the 2022 paper was an Accounts Assistant – Panchayat paper). Low priority — but the method is one line: a 3-period moving average for a month = mean of that month and the months either side.
✅ WHAT THE NOTES DO EXCEPTIONALLY WELL
| Topic | Verdict |
|---|---|
| (viii) Index Numbers | ⭐ Outstanding. Laspeyres, Paasche, Fisher = √(L×P), and all four Tests of Adequacy (Unit, Time Reversal, Factor Reversal, Circular) with which method satisfies which. This was the hardest question in 2024 (Q78) and the notes fully cover it |
| (vii) Theory of Attributes | ⭐ (AB) = (A)(B)/N for independence, proportion method, Yule's coefficient, consistency, contingency tables — complete |
| (x) Vital Statistics | ⭐ CBR, GFR, SFR, TFR, CDR, SDR, STDR, GRR vs NRR with the mortality/survival distinction — complete for 2024·Q80 |
| (ii)/(iii) Collection & questionnaires | ⭐ ~390 lines; the Pre-test (Pilot survey) step is in the construction flowchart — exactly what 2024·Q73 rewarded |
| (iv) Tabulation | ⭐ Parts of a table, types, graphs, ogives, true/open-end classes. Explicitly "rows and columns" — which is why 2024·Q74's false statement ("rows and not columns") is catchable |
📊 SCORECARD — the 20 PYQs against these notes
| Outcome | Count | Questions |
|---|---|---|
| ✅ Fully answerable | 10 | 2024: Q71, Q72, Q73, Q74, Q75, Q77, Q78, Q80 · 2022: Q35, Q39 |
| ⚠️ Risky (fact wrong or definition off) | 3 | 2024: Q79 (simultaneity gloss) · 2022: Q36 (940 vs 943), Q38 (polygon limit) |
| ❌ Cannot answer | 4 | 2024: Q76 · 2022: Q34 (both probability), Q31 (sampling error), Q40 (Nagaland) |
| ➖ Off-syllabus (Maths / time series) | 3 | 2022: Q32, Q33, Q37 |
As written, these notes would score about 10–13 of 17 in-syllabus marks. Add Probability and the four small gaps above and they become a complete 10/10 resource — the index-numbers and attributes sections are already stronger than anything a coaching handout gives you.
