Statistics 2024 Paper II 50 marks Compulsory Discuss

Q5

(a) Discuss the Indian Statistical System. State some important organisations and explain the main working of the National Statistical Organisation (NSO). 10 marks (b) Consider AR(1) model with non-zero mean 74·3293 and φ = 0·5705. If the last observed value is 67, then obtain the forecasting 1 time unit into the future yields. What is the forecasted value of 5 time units into the future ? 10 marks (c) Discuss the concept of structure and model for Simultaneous Linear Statistical Equations (SLSE) model. The application of least squares method for estimating the parameters in SLSE model is inappropriate. Explain. 10 marks (d) (i) Determine the average age at death of those who die between ages x and x + n. (ii) If l(x) = 100√(100 – x) find μ(84) exactly using appropriate method. 10 marks (e) What are intelligence tests and how are they used in measuring intelligence ? Define the terms mental age and IQ in this connection. 10 marks

हिंदी में प्रश्न पढ़ें

(a) भारतीय सांख्यिकीय पद्धति पर चर्चा कीजिए । कुछ महत्वपूर्ण संस्थाएँ बताइए तथा राष्ट्रीय सांख्यिकीय संगठन (एन एस ओ) के प्रमुख प्रकार्यों को समझाइए । 10 (b) एक AR(1) मॉडल पर विचार कीजिए जिसका शून्येतर माध्य 74·3293 और φ = 0·5705 है । यदि अंतिम प्रेक्षित मान 67 है, तो भविष्य उपज में 1 समय इकाई पूर्वानुमान प्राप्त कीजिए । भविष्य में 5 समय इकाइयों का पूर्वानुमानित मान क्या है ? 10 (c) युगपत रैखिक सांख्यिकीय समीकरण (एस एल एस ई) मॉडल के लिए संरचना तथा मॉडल की संकल्पना की चर्चा कीजिए । एस एल एस ई मॉडल में प्राचलों का आकलन करने के लिए न्यूनतम वर्ग विधि का अनुप्रयोग अनुचित है । समझाइए । 10 (d) (i) जिनकी मृत्यु, आयु x और x + n के बीच होती है, उनकी मृत्यु के समय औसत आयु ज्ञात कीजिए । (ii) यदि l(x) = 100√(100 – x) है, तो उपयुक्त विधि का उपयोग करके μ(84) का यथार्थ मान ज्ञात कीजिए । 10 (e) बुद्धि परीक्षण क्या हैं और बुद्धि को मापने में ये कैसे उपयोग किए जाते हैं ? इस संबंध में मानसिक आयु तथा बौद्धिक स्तर (आई क्यू) पदों को परिभाषित कीजिए । 10

Evaluate your answer to this question → See all 2024 Statistics questions

Directive word: Discuss

This question asks you to discuss. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

This multi-part question requires balanced coverage across five thematic areas. Allocate approximately 20% time each to parts (a), (c), and (e) which demand descriptive-discursive treatment, and 20% combined to parts (b) and (d) which require precise calculations. Begin with a brief roadmap indicating coverage of all sub-parts, then proceed sequentially: Indian statistical infrastructure → AR(1) forecasting with proper formula application → SLSE theoretical exposition → life table computations with force of mortality derivation → psychometric concepts with Binet-Simon/Wechsler references. Conclude each calculation part with interpreted results in context.

Key points expected

  • (a) Indian Statistical System: Evolution from PC Mahalanobis era; distinction between Central and State statistical machinery; NSO's role under Ministry of Statistics and Programme Implementation (MoSPI); key organizations—CSO, NSSO, Registrar General of India, NITI Aayog; NSO's functioning through data collection, coordination, and dissemination under National Statistical Commission oversight
  • (b) AR(1) forecasting: Correct model specification X_t = μ + φ(X_{t-1} - μ) + ε_t; one-step ahead forecast = μ + φ(x_n - μ) = 74.3293 + 0.5705(67 - 74.3293); five-step ahead forecast converges to mean μ as φ^5 → 0; explicit numerical computation
  • (c) SLSE model: Structural form vs reduced form distinction; endogeneity problem causing correlation between regressors and error terms; simultaneous equation bias; why OLS is inconsistent (covariance between Y and u non-zero); need for IV/2SLS methods
  • (d)(i) Average age at death: n_a_x = (∫_0^n (x+t)μ(x+t)l(x+t)dt)/(l(x)-l(x+n)) or equivalent life table expression; (d)(ii) Force of mortality μ(x) = -d[ln l(x)]/dx; exact derivation for l(x)=100√(100-x) yielding μ(84)=1/32
  • (e) Intelligence tests: Definition as standardized measures of cognitive ability; types—verbal, performance, group vs individual; uses in education, clinical diagnosis, occupational selection; mental age (MA) as performance level relative to age norms; IQ formulas—Stern's ratio IQ (MA/CA×100) and deviation IQ; reference to Indian adaptations

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Setup correctness20%10For (a): Accurately identifies NSO's 2019 merger structure and hierarchical data flow; for (b): Correctly writes AR(1) model with non-zero mean and identifies forecast formula; for (d): Properly sets up life table integral and force of mortality definition; no conceptual confusion between structural and reduced forms in (c)Basic identification of organizations in (a) with minor errors in NSO functioning; AR(1) model stated but mean handling unclear; life table notation present but integral setup incomplete; SLSE structure mentioned without clear endogeneity explanationConfuses NSO with NSSO or CSO; writes AR(1) as X_t = φX_{t-1} ignoring mean; omits force of mortality definition entirely; fails to distinguish structural from reduced form
Method choice20%10For (b): Applies conditional expectation E[X_{n+h}|X_n] correctly with geometric decay; for (d): Selects exact differentiation over approximation for μ(x); for (c): Explains why OLS fails (simultaneity bias) and identifies need for instrumental variables; appropriate Indian statistical examples in (a)Correct general approach to forecasting but algebraic steps unclear; computes μ(x) numerically rather than analytically; mentions bias in SLSE without explaining covariance mechanism; adequate but generic organizational examplesUses unconditional mean for all forecasts; attempts discrete approximation for continuous mortality; suggests OLS is appropriate for SLSE; no specific Indian examples or outdated pre-2019 structure
Computation accuracy20%10Precise arithmetic: (b) One-step forecast = 70.15 (approx), five-step = 74.33 (mean); (d)(ii) μ(84) = 1/32 = 0.03125 exactly; all intermediate steps shown with proper handling of negative values and exponentsCorrect formulas but arithmetic errors in final decimals; approximate μ(84) without exact fraction; forecast values reasonable but rounding inconsistent; partial credit for correct methodologyMajor calculation errors (e.g., sign errors in AR(1), division by zero in mortality); no working shown; answers inconsistent with stated parameters; omits part (d)(i) entirely
Interpretation20%10Interprets AR(1) forecasts showing mean reversion property; explains why five-step forecast approaches μ; contextualizes average age at death within life table analysis; connects SLSE issues to real-world econometric applications (supply-demand, Keynesian models); evaluates intelligence test limitations and cultural bias in Indian contextStates numerical results without explaining economic/statistical meaning; brief mention of mean reversion; generic statement about OLS inappropriateness; standard definitions without critical evaluation of IQ testingNo interpretation of results; fails to explain why forecasts change with horizon; ignores practical implications of simultaneous equations; purely definitional treatment of intelligence tests
Final answer & units20%10All five sub-parts addressed with clear final answers: (a) comprehensive organizational list with NSO workflow; (b) both forecasts boxed with 2-4 decimal precision; (c) explicit conclusion on OLS inappropriateness; (d)(i) symbolic expression for average age, (d)(ii) exact value 1/32 or 0.03125; (e) precise MA and IQ definitions with formulas; proper units (years, mortality rate per year)Most parts answered but one sub-part incomplete or vague; forecasts present but precision inconsistent; average age at death formula without simplification; IQ definition without formulaMultiple sub-parts missing or severely incomplete; no boxed final answers; units omitted or incorrect; confusion between mental age and chronological age definitions

Practice this exact question

Write your answer, then get a detailed evaluation from our AI trained on UPSC's answer-writing standards. Free first evaluation — no signup needed to start.

Evaluate my answer →

More from Statistics 2024 Paper II