Source document. This page reproduces the syllabus this course was written to, as published — its semesters, credits and paper numbers are that document’s, not this site’s. The course itself is studied on its own, in any order.

Course Information

Title	Applied Statistics
Theory Credits	3 (3 hrs/week)
Practical Credits	1 (2 hrs/week)

Course Outcomes

1. Master forecasting techniques and their applications.
2. Interpret and use a range of index numbers commonly used in business.
3. Perform calculations involving simple and weighted index numbers.
4. Understand the basic structure of the Consumer Price Index and perform calculations involving its use.
5. Apply various data-collection methods for better policy insight.
6. Construct and implement life tables.
7. Use population growth curves, estimates and projections.
8. Implement demographic concepts on real data through practicals.

Theory — Five Units

Unit 1: Time Series

Time series and its components with illustrations; additive, multiplicative and mixed models. Trend — estimation by free-hand curve method, semi-averages, least squares (linear and parabolic), moving averages method.

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Unit 2: Seasonal Component

Determination of seasonal indices by Simple Averages method, Ratio to Moving Average, Ratio to Trend and Link Relatives methods; deseasonalisation.

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Unit 3: Index Numbers

Concept, construction, problems, uses and limitations of index numbers. Simple and weighted index numbers — various weighted aggregate index numbers; criteria of a good index number; Fisher's ideal index. Cost of living index and wholesale price index.

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Unit 4: Vital Statistics

Introduction, definition and uses of vital statistics; sources of vital statistics. Measures of mortality rates — Crude Death Rate, Specific Death Rate, Standardised Death Rate with different populations and problems.

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Unit 5: Life Tables & Fertility

Life table — columns, construction and uses of life table; proofs of life-table functions. Measures of fertility rates — Crude Birth Rate, General Fertility Rate, Age-Specific Fertility Rate, Total Fertility Rate. Measures of population growth — Pearl's vital index, Gross Reproduction Rate, Net Reproduction Rate and related problems.

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Practical — List of Experiments (13)

1. Measurement of trend by moving averages (odd and even period).
2. Measurement of trend by least squares (linear and parabolic).
3. Determination of seasonal indices by method of simple averages.
4. Determination of seasonal indices by Ratio to Moving Averages.
5. Determination of seasonal indices by Ratio to Trend.
6. Determination of seasonal indices by Link Relatives.
7. Computation of simple index numbers.
8. Computation of all weighted index numbers.
9. Computation of reversal tests.
10. Computation of various mortality rates.
11. Computation of various fertility rates.
12. Computation of various reproduction rates.
13. Construction of a life table.

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Text Books / References

1. V. K. Kapoor & S. C. Gupta — Fundamentals of Applied Statistics, Sultan Chand & Sons.
2. P. Mukopadhyay (2011) — Applied Statistics, 2nd ed., Books and Allied Pvt. Ltd.
3. P. J. Brockwell & R. A. Davis (2003) — Introduction to Time Series Analysis, Springer.
4. C. Chatfield (2001) — Time Series Forecasting, Chapman & Hall.
5. K. Srinivasan (1998) — Demographic Techniques and Applications, Sage Publications.
6. O. S. Srivastava (1983) — A Text Book of Demography, Vikas Publishing House.

Suggested Co-Curricular Activities

1. Training of students by related industrial experts.
2. Assignments including technical assignments, if any.
3. Seminars, group discussions, quiz, debates etc. on related topics.
4. Preparation of audio and videos on tools of diagrammatic and graphical representations.
5. Collection of material / figures / photos of related topics.
6. Invited lectures and presentations of stalwarts on those topics.
7. Visits / field trips of firms, research organizations etc.

Exam Blueprint (recommended)

Unit	Topic	Approx. Weightage
1	Time Series	20 %
2	Seasonal Component	20 %
3	Index Numbers	25 %
4	Vital Statistics (Mortality)	15 %
5	Life Tables, Fertility & Growth	20 %

Quick Reference — Key Formulas

Item	Formula
Linear trend (centred X)	\(a = \bar Y,\; b = \sum XY / \sum X^2\)
Laspeyres	\(\sum p_1 q_0 / \sum p_0 q_0 \times 100\)
Paasche	\(\sum p_1 q_1 / \sum p_0 q_1 \times 100\)
Fisher	\(\sqrt{P^L \cdot P^P}\)
CDR	\(D / P \times 1000\)
ASDR	\(D_x / P_x \times 1000\)
CBR	\(B / P \times 1000\)
GFR	\(B / P^f_{15-49} \times 1000\)
TFR	\(\sum \text{ASFR}_x \times n / 1000\)
GRR	\(\text{TFR} \times f\) (\(f \approx 0.487\))
NRR	\(\sum \text{ASFR}_x \cdot f \cdot (L_x / l_0) \cdot n / 1000\)
Life expectancy	\(e_x = T_x / l_x\)