Module Title:             Foundations of Statistics.

Module code:              AMT102

Semester:                     III

Credit Value:              12

Module Writer:           Mr. Rinzin Namgyel and Mr. Thinley Namgyel

General Objective:   

Knowledge in Statistics is essential in this information age. Very often we come across

data that needs to be analyzed and interpreted so that they could make better decision. For

that knowledge of Statistics becomes imperative. This module aims to provide basic

knowledge and skills of statistics to the students.

Learning outcomes:

At the end of the course, the students will be able to:

·         Express the scope of statistics in day to day life

·         Organize different kinds of data and represent them by various methods like tables, charts etc.

·         Evaluate various measures like central tendency, dispersion etc. and explain their properties and uses.

·         Analyze and interpret data and make conclusions.

·         Use statistical software like SPSS and Excel.

·         Apply all the concepts in real time situations.

Learning and Teaching Approaches:

There will be at least four lectures and a lab session in a week. Assignments will be given on a regular basis to keep track of the students’ understanding. Two major assignments will be evaluated as part of continuous assessment.

Method of assessment

Written assignment                 10%

Lab assignments                      10%

Mid-term Examination            20%

Final Examination                   60%

Subject Matter

1.      INTRODUCTION TO STATISTICS:

 Definition and scope of Statistics, Descriptive Statistics vs. Inferential Statistics, types of data: nominal, ordinal, scalar data, Qualitative and Quantitative data, Variables: Discrete vs. Continuous variables. (2 Lectures)

2.      DATA ORGANIZATION:

Raw data, Ordered Array, Frequency Distribution: type and construction of frequency distribution tables, Graphical representation of frequency distribution: Histogram, Frequency Polygon, Cumulative frequency curve or the Ogives. (3Lectures)

3.      MEASURES OF CENTRAL TENDENCY AND DISPERSION:

Arithmetic mean and its properties, Median,  Mode, Relationship between Mean, Median and Mode, Geometric mean, Quartiles, Deciles and Percentiles, The Range, Quartile Deviation, Mean Deviation, Variance, Properties of Variance, Standard Deviation, Application of Standard Deviation, Relationship between the measures of dispersion, Coefficient of variation.  (10 L)

4.      MEASURES OF SKEWNESS AND KURTOSIS:

Pearsonian Measure of Skewness, Bowley’s Measure of Skewness, Moment Coefficient of Skewness, Moment Coefficient of Kurtosis, Percentile Coefficient of Kurtosis. (5 L)

5.      ANALYSIS OF MULTIVARIATE DATA:

Bi-variate data and scatter diagram, Principle of least square and curve fitting, Correlation and regression, partial and multiple correlation coefficients. (5L)

6.      THEORY OF PROBABILITY:

The nature of probability, some important definitions and examples, Basic rules of probability, Theorems on probability (without proof). (2L)

7.      PROBABILITY DISTRIBUTIONS:           

Random variables, Discrete probability distributions (without proof): Binomial distribution, Poisson distribution, Continuous probability distributions (without proof): Uniform distributions, exponential and normal distributions. (5L)

8.      SAMPLING DISTRIBUTIONS:

The rationale for sampling, Sample statistics, Random Sampling, sampling distributions, sampling distributions of the Mean, sample variance from a normal population. (5L)

9.      HYPOTHESIS TESTING:

The rationale for hypothesis testing, general procedure for hypothesis testing, the null and alternative hypothesis, One-tailed and Two-tailed tests, Errors in hypothesis testing, Critical region, level of significance of a test. (7L)

10.  TIME SERIES:

Calculation of Trends using moving average linear trend by method of least square, Exponential Trends ( of the form (Y=ab^x). Shifting of trends origin. Conversion of annual trends values to monthly values. Measurement of Seasonal variation by ratio to trend method. Deseasoniing of the series. Forecasting. (6L)

List of Practicals:

1.      Statistical functions in Excel.

2.      Calculation of various measures for a given set of data using Excel.

3.      Charts and graphs in Excel

4.      Multiple correlation using Excel

5.      Regression and multiple regression in Excel

6.      Defining variables and data entry in SPSS

7.      Data manipulation in SPSS

8.      Descriptive statistics, correlation and regression using SPSS

9.      Graphs and charts using SPSS

10.  Comparison of  means and interpretation of P-values using SPSS

Reading List:

Essential Reading:

1. Hooda, R.P. (1994). Statistics for Business and Economics. Macmillian India Ltd.
2. Braverman, J.D. (1978). Fundamentals of Business Statistics. New York: Academic Press Inc.
3. Kenny, J. F. & Keeping, E. S. (1974). Mathematics of Statistics, Volume 1.3rd Edition. Affiliated East-West Press Pvt. Ltd.
4. Freund, J. E. (2001). Mathematical Statistics. (5^th Edition). PHI
5. Mood, A. M, Graybill, F.A., and Bose, D.C. (2001). Introduction to the theory of Statistics. (3^rd Edition). TMH.

Suggested reading:

1.        Walpole, R. E.,  Myers, R. H.,  Myers, S. L. & Ye, K.  (2001). Probability and Statistics for Engineers and Computer Scientists. (7th Edition). Pearson Education.

2.       Spiegel, M. R., Srinivasan, R. A., & Schiller, J. J. (2000). Schaum's outline of theory and problems of probability and statistics. New York: McGraw-Hill.

3.        Goon, A.M, Gupta, M.K. & Das, G.B. (2002). Fundamentals of Statistics-Volume I and II. (5th Revised Edition). World Press Pvt. Ltd.

4.       Sheldon, M.R. (2007). Introduction to Probability Models.(9^th Edition), Academic Press.

(Updated June, 2013)