COURSE PLAN
Course: QUANTITATIVE TECHNIQUES (MB-104)
Instructor: Navin Chandra
Course Objectives: The course of ‘quantitative techniques’ is structured in such a way so that the student pursuing MBA should have knowledge of various types of data, techniques of analysis of data, hypothesis setting and decision making from test of hypothesis. After going through the subject, students will be able to how to use-
a) Mathematical Tools like Annuities, Depreciation, Compound Interest techniques;
b) Statistical Tools of Averages, Dispersion, Correlation, Regression, Time Series and Index Numbers;
c) Probability, Probability Distributions and Test of Hypothesis in the business environment.
SYLLABUS
Unit I (MATHEMATICS)
1. Role of Mathematics and statistics in Business Decisions
2. Theory of Sets
3. Compound interest, depreciation and annuities
4. Linear, Quadratic & Simultaneous Equations
5. Matrix Algebra
6. Binomial Theorem
7. Principles of Mathematical Induction
8. Arithmetic Progression & Geometric Progression
Unit II (MEASURES OF AVERAGES, DISPERSIONS & INDEX NUMBERS)
1. Measure of Central Tendency
2. Measures of Dispersion: Range, Quartile Deviation, Mean Deviation, Standard
Deviation and Coefficient of Variation, Skewness and Kurtosis
3. Index Numbers: Simple, Aggregated, Weighted and Tests of Index Numbers
Unit III (CORRELATION, REGRESSION AND TIME SERIES ANALYSIS)
1. Correlation Analysis: Rank Method & Karl Pearson's Coefficient of Correlation and Properties of Correlation.
2. Regression Analysis: Fitting of a Regression Line, Interpretation of Results,
Properties of Regression Coefficients, Relationship between Regression and
Correlation
3. Time Series Analysis: Trend Variation, Least Square Fit, Seasonal Variation
Unit IV (PROBABILITY, HYPOTHESIS TESTING)
1. Theory of Probability, Addition and Multiplication Law, Bayes’ Theorem
2. Theoretical Distributions: Binomial, Poisson and Normal Distribution
3. Sampling Distribution, Standard Error
4. Theory of Estimation, Point Estimation, Interval Estimation
5. Testing of Hypothesis: Large Sample Tests, Small Sample test, (t, F, Z Test and Chi Square Test).
Recommended Text Books:
S.No | Author | Title | Publisher |
1 | SANCHETI & KAPOOR | BUSINSESS MATHEMATICS | SULTAN CHAND & SONS |
2 | S.P. GUPTA | STATISTICAL METHODS | SULTAN CHAND & SONS |
3 | LEVIN & RUBIN | STATISTICS FOR MANAGEMENT | PRENTICE HALL INDIA |
Recommended Reference Books:
S.No | Author | Title | Publisher |
1 | Dr. S. C. AGGARWAL | BASIC MATHEMATICS FOR MBA | V K (INDIA) ENTERPRISES |
2 | ANDERSON, SWEENEY & WILLIAMS | STATISTICS FOR BUSINESS AND ECONOMICS | CENGAGE LEARNING |
3 | T. R. JAIN & Dr. S. C. AGGARWAL | STATISTICS FOR MBA | V K (INDIA) ENTERPRISES |
Case studies & their objectives:
Case 1: INDIAN CRICKETERS – EARNINGS CONSIDERING RUNS & WICKETS
The objective of this case study is to use statistical tools of Measures of- ‘Central Tendency’ and ‘Dispersion’ in practical situation.
Case 2: RELIANCE INDUSTRIES LTD- BETA COEFFICIENT
The objective of this case study is to find out BETA co-efficient of a Company using statistical tools of ‘Covariance’ and ‘Variance’.
Assignments:
Assignment 1: Sums from Unit 1 of the syllabus based on actual business situation.
Assignment 2: Calculation of co-efficient of correlation between SENSEX (BSE) and NIFTY (NSE) for-
a) Closing indices from 1st July,2010 to 15th July,2010
b) Market Capitalisation from 1st July,2010 to 15th July,2010
c) Daily rate of Return
The Objective of these assignments is that the students should adapt themselves how the calculations and analyses are made in real life situations.
Evaluation: Students will be evaluated on the basis of following criteria
MSE’s: 15 marks
Presentation: 7 marks
TESTS (two): 10 marks (Every test will have equal weightage of 5 marks)
Assignments (two): 8 marks (Each assignment will carry 4 marks)
LECTURE SCHEDULE
Lecture Number | Topics | Assignment |
1 | Theory of Sets 1. Definition of sets 2. Representation of sets- a) Tabular or Roster Form b) Set Builder Form 3. Types of sets | |
2 | Theory of Sets 1. Types of sets (contd...) 2. Elementary operations a) Union of two sets b) Intersection of two sets c) Complement of a set d) Difference of two sets e) Symmetric difference of two sets 3. Laws of set operations | |
3 | Compound Interest & depreciation a) Logarithms b) Compound interest sums c) Depreciation sums | |
4 | Annuities 1. Types of annuities 2. Sums of sum due | |
5 | Annuities Sums of present value | |
6 | Linear, Quadratic & Simultaneous Equations 1. Brief of equations & steps for solution 2. sums for solution of equations | |
7 | Matrix Algebra 1. Definition & Types of Matrices 2. Operations on Matrices | |
8 | Matrix Algebra 1. Determinant of Matrix 2. Inverse of Matrix | |
9 | Matrix Algebra 1. Solution of simultaneous =ns by Crammer rule 2. Solution of simultaneous =ns by Matrix method | |
10 | Binomial Theorem 1. Statement for Binomial Expansion 2. Sums of binomial expansion | |
11 | Principles of Mathematical Induction 1. Working Rule for proving statement 2. Sums of mathematical induction | Assignment 1- sums from unit 1 of syllabus |
12 | Arithmetic Progression & Geometric Progression 1. Rule of A.P. 2. Finding out nth term and sum of n terms | |
13 | Arithmetic Progression & Geometric Progression 1. Rule of G.P. 2. Finding out nth term and sum of n terms | |
14 | Measure of Central Tendency Definition and formulae of Mean, Median & Mode | |
15 | Measures of Dispersion 1. Range and its co-efficient 2. Quartile Deviation and its co-efficient | |
16 | Measures of Dispersion 1. Mean Deviation and its co-efficient | |
17 | Measures of Dispersion 1. Standard Deviation and Coefficient of Variation | |
18 | Case Study 1 to be discussed | |
19 | Measures of Skewness and Kurtosis | |
20 | Index Numbers 1. Simple aggregated index numbers 2. Simple average index numbers 3. Weighted aggregated index numbers 4. Tests of Index Numbers | |
21 | Index Numbers 1. Weighted aggregated index numbers 2. Weighted average index numbers 3. Tests of Index Numbers | |
22 | Correlation Analysis 1. Definition 2. Karl Pearson's Coefficient of Correlation | |
23 | Correlation Analysis 1. Karl Pearson's Coefficient of Correlation | |
24 | Correlation Analysis 1. Spearman’s Rank correlation 2. Properties of correlation | Assignment 2- Calculation of co-efficient of correlation between BSE & NSE |
25 | Case Study 2 to be discussed | |
26 | Regression Analysis 1. Fitting of a Regression Line | |
27 | Regression Analysis 1. Fitting of a Regression Line | |
28 | Regression Analysis 1. Properties of Regression Coefficients 2. Relationship between Regression and Correlation | |
29 | Time Series Analysis 1. Trend Variation- semi average method 2. Trend Variation- moving average method | |
30 | Time Series Analysis Trend Variation- Least square method | |
31 | Time Series Analysis Seasonal Variation- a) Method of Simple Average; b) Method of Moving Average c) Ratio to Moving Average | |
32 | Time Series Analysis Seasonal Variation- Ratio to Trend Method | |
33 | Time Series Analysis Seasonal Variation- Link Relatives Method | |
34 | Theory of Probability 1. Definition 2. Addition and Multiplication Law 3. Sums of probability | |
35 | Theory of Probability 1. Sums of probability | |
36 | Theory of Probability 1. Bayes’ Theorem | |
37 | Theoretical Distributions 1. Binomial Distribution 2. Sums of Binomial Distribution | |
38 | Theoretical Distributions 1. Poisson Distribution 2. Sums of Poisson Distribution | |
39 | Theoretical Distributions 1. Normal Distribution 2. Sums of Normal Distribution | |
40 | Sampling Distribution & Standard Error | |
41 | Theory of Estimation 1. Point Estimation 2. Interval Estimation | |
42 | Testing of Hypothesis Large Sample Tests- Z test | |
43 | Testing of Hypothesis Large Sample Tests- Z test | |
44 | Testing of HypothesisSmall Sample Tests- t test | |
45 | Testing of HypothesisSmall Sample Tests- t test | |
46 | Testing of Hypothesis Chi Square Test | |
47 | Testing of Hypothesis F test & ANOVA Table | |
48 | Testing of Hypothesis ANOVA Table |
CASE STUDY-1
INDIAN CRICKETERS – EARNINGS CONSIDERING RUNS & WICKETS
A report, published in newspaper The Times of India on 12th November, 2006, showed the following data of earnings, runs scored and wickets taken by some of international cricketers in the year in one day matches in 2005-06:
S. No. | Name of Cricketer | Earnings (Rs. In Lac) | Runs Scored | Earning per run (Rs) | Wickets Taken | Earnings per wicket (Rs) |
BATSMEN | ||||||
1 | Rahul Dravid | 138.50 | 2,371 | 5,841 | 0 | 0 |
2 | Sachin Tendulkar | 102.90 | 1,063 | 9,680 | 3 | 34,30,000 |
3 | Virender Sehwag | 133.70 | 1,793 | 7,457 | 19 | 7,03,684 |
4 | V. V. S. Laxman | 77.50 | 589 | 13,158 | 0 | 0 |
5 | Sourav Ganguly | 60.00 | 155 | 38,710 | 1 | 60,00,000 |
6 | Yuvraj Singh | 112.10 | 1,619 | 6,924 | 8 | 14,01,250 |
7 | Mohd. Kaif | 88.40 | 708 | 12,486 | 0 | 0 |
8 | Gautam Gambhir | 45.10 | 350 | 12,886 | 0 | 0 |
9 | Suresh Raina | 43.20 | 516 | 8,372 | 0 | 0 |
10 | Wasim Jaffer | 17.50 | 622 | 2,814 | 0 | 0 |
BOWLERS | ||||||
11 | Anil Kumble | 82.50 | 355 | 23,239 | 68 | 1,21,324 |
12 | Harbhajan Singh | 91.88 | 357 | 25,737 | 66 | 1,39,212 |
13 | Irfan Pathan | 119.80 | 986 | 12,150 | 71 | 1,68,732 |
14 | Ajit Agarkar | 91.40 | 188 | 48,617 | 46 | 1,98,696 |
15 | Zaheer Khan | 31.40 | 56 | 56,071 | 13 | 2,41,539 |
16 | Munaf Patel | 51.00 | 38 | 1,34,211 | 33 | 1,54,545 |
17 | Sreesanth | 62.90 | 78 | 80,641 | 45 | 1,39,778 |
WICKETKEEPER | ||||||
18 | M. S. Dhoni | 120.30 | 1,587 | 7,580 | 0 | 0 |
Mahesh wants to analyse the above data to evaluate the performance of these players. He has thought of using the measures of location (central tendency) and measures of dispersion for this analysis. He wants to calculate:
a) Average Earnings per run scored for the batsmen;
b) Average Earnings per wicket taken for the bowlers;
c) Appropriate measure of consistency among the batsmen with respect to earnings per run;
d) Appropriate measure of consistency among the bowlers with respect to earnings per wicket.
You are required to help Mahesh in above analysis and evaluate their performances.
* * * * *
CASE STUDY-2
RELIANCE INDUSTRIES LTD- BETA COEFFICIENT
Mr. Jagmohan, Managing Director of J.M. Securities Limited, a stock exchange brokering company, is interested in investing huge funds in the equity shares of RELIANCE INDUSTRIES LTD. The equity share of the above company is currently being traded at Rs. 1,208. He wants to find out whether the share is over-valued or under-valued. For this purpose he has obtained and analysed various relevant information like risk free rate of return, rate of return on market portfolio and estimated cash inflows for next ten years. Now he needs to find out Beta Co-efficient of the Company. For this purpose the following information is provided:
Date | BSE Sensex | Market Price of RIL |
5.10.2006 | 12389 | 1155 |
6.10.2006 | 12373 | 1163 |
9.10.2006 | 12366 | 1154 |
10.10.2006 | 12364 | 1151 |
11.10.2006 | 12353 | 1143 |
12.10.2006 | 12538 | 1170 |
13.10.2006 | 12736 | 1190 |
16.10.2006 | 12928 | 1213 |
17.10.2006 | 12884 | 1216 |
18.10.2006 | 12858 | 1208 |
You are required to help out Mr. Jagmohan in finding out β of Reliance Industries Limited. The following formulae may be of your help:
1. Daily Rate of Return= *100
2. β =
* * * * *
