FAA Statistics — Detailed Study Plan
📊 FAA STATISTICS — The 10-Mark Plan
Section: Statistics · 10 of 120 marks · 10 syllabus topics · 1 question each Companion: Statistics-Analysis-and-Mapping (the evidence) · Statistics-Tagged-Answers (all 20 solved)
The 2024 paper asked exactly one question from each of the 10 syllabus topics, in order. That makes Statistics the most predictable section on the entire paper — you know precisely how many questions come from where. Total study time needed: ~12–14 hours for 10 marks. Compare that to Maths, which needs far more time for the same 10 marks. ⭐ Realistic target: 8–9 / 10.
PART 1 — The strategy in one box
- Never skip a topic. One skipped topic = exactly one lost mark, guaranteed. There is nowhere to hide.
- Never over-study a topic. Only one question comes from each — depth beyond that is wasted time.
- Breadth beats depth. Cover all 10 shallowly before deepening any one.
What that means practically: spend roughly 1–1.5 hours per topic, not 5 hours on probability and none on index numbers.
PART 2 — Topic-by-topic: what to learn and how long
🟢 EASY TIER — pure recall (4 hrs total, ~4 marks)
(i) Primary & Secondary Data · 1 hr
Learn the definitions and the split:
| Primary | Secondary |
|---|---|
| First-hand, collected by you | Already exists, collected by others |
| Interviews, surveys, questionnaires, observation, experiments | Government publications, census, journals, websites, company records |
| Costly, slow, reliable, specific | Cheap, fast, may not fit your need |
⭐ The test: go out and get it yourself → primary · look it up → secondary.
(ii) Methods of Collecting Data · 1 hr
- Primary methods: direct personal interview, indirect oral investigation, questionnaire (mailed / through enumerators), schedules, observation
- Secondary sources: published (government reports, census, journals) and unpublished (records, diaries)
- ⭐ Sampling error decreases as sample size increases; a census has no sampling error
- Census vs Sample: census = complete enumeration; sample = a part
(iii) Preparation of Questionnaires · 1 hr
- Characteristics: short, simple, unambiguous, logically ordered, non-leading
- ⭐ A PILOT TEST (pre-test) is essential — statements saying "skip the pilot test" are always wrong
- ⭐ Decide the order/flow first, then refine individual wording
- Design drives validity, reliability and response rate
- Avoid: leading questions, double-barrelled questions, personal/embarrassing items
(ix) Demography — Census · 1 hr
⭐ Features: Simultaneity · Universality · Periodicity (10 years) · Government sponsorship · Individual enumeration · Defined territory
Census 2011 — memorise these:
| Fact | Value |
|---|---|
| Population | 121.09 crore |
| Decadal growth | 17.7% |
| Density | 382 / km² |
| Sex ratio | 943 females per 1000 males |
| Literacy | 74.04% |
| Most / least populous state | UP / Sikkim |
| Highest / lowest literacy | Kerala / Bihar |
| ⭐ Only state with negative growth | Nagaland (−0.58%) |
| First census / first regular census | 1872 / 1881 |
🟡 MODERATE TIER — light calculation (5 hrs, ~4 marks)
(iv) Tabulation & Compilation · 1 hr
- Parts of a table: table number, title, caption (column heads), stub (row heads), body, head-note, foot-note, source
- ⭐ Tabulation precedes diagrammatic representation
- Tables allow comparison across BOTH rows and columns (the 2024 false statement said "rows and not columns")
- Graphs: histogram · frequency polygon · ogive (cumulative frequency curve)
- ⭐ As classes increase, a frequency polygon smooths into a frequency curve
(v) Measures of Central Tendency · 1.5 hrs
| Measure | Formula |
|---|---|
| Mean | Σx ÷ n |
| Median | middle value; if n is even → average of the two middle values |
| Mode | most frequently occurring value |
| ⭐ Empirical relation | Mode = 3 Median − 2 Mean |
Also know: mean is affected by extreme values; median is not · a data set can have no mode or several · for a symmetric distribution Mean = Median = Mode. Practise: compute all three from a small raw data set in under 60 seconds (exactly what 2024·Q75 wanted).
(vi) Theory of Probability · 1.5 hrs
0 ≤ P(A) ≤ 1 · impossible event = 0 · certain event = 1 · P(A) + P(Ā) = 1
| Rule | Formula |
|---|---|
| Addition | 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) |
⚠️ The trap to know: mutually exclusive events sum to 1 only if they are also exhaustive. ⭐ Exam shortcut: any option greater than 1 cannot be a probability — eliminate it instantly.
(vii) Theory of Attributes · 1 hr
- Attribute = a qualitative characteristic (blindness, literacy, gender) — not measurable numerically
- Notation: (A) = frequency of A · (AB) = ultimate class frequency
- ⭐ If A and B are INDEPENDENT: (AB) = (A) × (B) ÷ N
- Association:
| Condition | Meaning |
|---|---|
| (AB) > (A)(B)/N | Positive association |
| (AB) < (A)(B)/N | Negative association (disassociation) |
| (AB) = (A)(B)/N | Independent |
- Consistency: no class frequency may be negative
- Also practise Venn-style counting (the 2024 boys/girls grid) — build a 2-way table and fill the gaps
🔴 HARD TIER — do these properly (4 hrs, ~2 marks)
(viii) Theory of Index Numbers · 2 hrs ⭐ the hardest question in 2024
| Index | Formula / basis |
|---|---|
| Laspeyres | uses base-year quantities (q₀) |
| Paasche | uses current-year quantities (q₁) |
| ⭐ Fisher's Ideal | √(Laspeyres × Paasche) — the geometric mean |
| Value Index | Price Index × Quantity Index |
The two tests — know why Fisher is "ideal":
| Test | Condition |
|---|---|
| ⭐ Time Reversal | P₀₁ × P₁₀ = 1 |
| ⭐ Factor Reversal | P₀₁ × Q₀₁ = Value Index |
⭐ Fisher's Ideal Index satisfies BOTH — that is exactly why it is called ideal. Laspeyres and Paasche satisfy neither. The 2024 trick: an index given the "wrong way round" is inverted by the time-reversal test — quantity index 0.5 for 1990/base-1993 → 1 ÷ 0.5 = 2 for 1993/base-1990.
Also know: CPI (consumer price index — cost of living, retail) vs WPI (wholesale price index) · base year should be normal and recent.
(x) Vital Statistics · 2 hrs
| Measure | What it is |
|---|---|
| CBR (Crude Birth Rate) | births per 1,000 population |
| CDR (Crude Death Rate) | deaths per 1,000 population |
| ASFR (Age-Specific Fertility Rate) | births per 1,000 women in an age group; ⭐ modal value 20–25 |
| TFR (Total Fertility Rate) | average children per woman over her reproductive life |
| ⭐ GRR (Gross Reproduction Rate) | average DAUGHTERS per woman — ⭐ IGNORES mortality |
| ⭐ NRR (Net Reproduction Rate) | GRR adjusted FOR mortality → ⭐ NRR ≤ GRR always |
| IMR (Infant Mortality Rate) | infant deaths per 1,000 live births |
| MMR (Maternal Mortality Ratio) | maternal deaths per 1,000 / 1,00,000 live births |
⭐ The one distinction that gets tested: GRR ignores mortality · NRR accounts for it. NRR = 1 → the population is exactly replacing itself.
PART 3 — The 5-week schedule
Statistics sits in Week 9 of FAA-MASTER-PLAN, but it is better spread thin than crammed. Do 2–3 hours a week alongside your main sections.
| Week | Topics | Hrs | Checkpoint |
|---|---|---|---|
| 1 | (i) Primary/Secondary · (ii) Collection methods | 2 | Can you classify any source as primary or secondary instantly? |
| 2 | (iii) Questionnaires · (iv) Tabulation | 2 | Name the parts of a table; know why a pilot test matters |
| 3 | (v) Central tendency · (vi) Probability | 3 | Compute mean/median/mode from raw data in <60 s |
| 4 | (vii) Attributes · (ix) Census | 2 | (AB)=(A)(B)/N by heart; recite Census 2011 figures |
| 5 | ⭐ (viii) Index Numbers · (x) Vital Statistics | 4 | Fisher = √(L×P); GRR vs NRR |
| Final | Re-solve all 20 PYQs from Statistics-Tagged-Answers | 1 | 18+/20 |
PART 4 — Formula sheet (the whole section on one page)
Mean = Σx ÷ n · Median = middle (even n → average of two middle) · Mode = most frequent ⭐ Mode = 3 Median − 2 Mean
0 ≤ P(A) ≤ 1 · P(A∪B) = P(A) + P(B) − P(A∩B) · independent → P(A∩B) = P(A)·P(B)
⭐ Independent attributes: (AB) = (A)(B) ÷ N
⭐ Fisher's Ideal = √(Laspeyres × Paasche) · Value Index = Price Index × Quantity Index Time Reversal: P₀₁ × P₁₀ = 1 · Factor Reversal: P₀₁ × Q₀₁ = Value Index
CBR / CDR per 1,000 population · IMR / MMR per 1,000 live births ⭐ GRR ignores mortality · NRR includes it · NRR ≤ GRR · NRR = 1 → replacement level
Census: Simultaneity · Universality · Periodicity (10 yrs) · Government sponsorship
PART 5 — Exam-day approach
10 questions, ~8 minutes. Statistics sits with the slower sections, so attempt it in your second pass — after GK and theory, before Maths.
| Order | Do |
|---|---|
| 1st | The definition/recall questions — primary/secondary, collection methods, census features. 10 seconds each |
| 2nd | Statement-based ("which are correct / which is FALSE") — judge each statement separately; one clearly-wrong statement usually kills two options |
| 3rd | Short sums — mean/median/mode, probability, (AB)=(A)(B)/N |
| Last | Index numbers and matching questions — the slowest |
- Any probability option greater than 1 is impossible — in 2022·Q34 that removed three of four options outright.
- In matching questions, anchor on the one pair you are sure of and eliminate every option that contradicts it.
Negative marking: at −0.25, attempt anything where you can eliminate even one option. Given how definition-heavy this section is, you should be attempting all 10.
PART 6 — Common traps seen in the two papers
| Trap | Guard |
|---|---|
| Stem asks for the FALSE / INCORRECT statement | Underline the word before answering (2024·Q74) |
| Probability options > 1 | Impossible — eliminate free (2022·Q34) |
| Index given with the base reversed | Invert it: 1 ÷ index (2024·Q78) |
| Mutually exclusive ≠ exhaustive | They sum to 1 only if exhaustive (2024·Q76) |
| "Probabilities can never be zero" | False — an impossible event is exactly 0 |
| Sex ratio convention | India's official = females per 1,000 males (943); some questions invert it — check the options |
| Direct expenses already inside a total | Don't subtract twice |
| GRR vs NRR | GRR ignores mortality; NRR includes it |
It is an Accounts Assistant (Panchayat) paper with a different syllabus — 3 of its 10 "statistics" questions were actually Mathematics (set theory, coordinate geometry) plus one time-series item. Do not use it to define your scope. The 2024 paper, which maps perfectly onto the 10 FAA topics, is the reliable guide.
