Quantitative Methods

1. Quantitative Methods Essential Basics varsha varde

2. Varsha Varde\ • M. Sc; Ph. D. in Statistics (O. R.) • Taught Advanced Stats to PG Students • Quantitative Faculty in NIBM • Visiting Faculty at JBIMS • Officer in Bank Of India • General Manager At AFC • Handled consultancy in Various Fields varsha varde 2

3. QUANTITATIVE METHODS • It is a broad term • Two branches of relevance to us are statistics and operations research • Each of these offers several tools and techniques to tackle real life problems in scientific manner varsha varde

4. STATISTICS • Word derived from Latin word status • It came into existence as collection of certain data of states • It continued to expand its boundaries to include planning and organising of data collection ,analysis of data and drawing meaningful conclusions from data • Data are input, statistics is process and information is output varsha varde

5. TOOLS IN STATISTICS Broadly classified into • Descriptive statistics-describes principal features of the collected data • Inferential statistics-says something about future or for present but for larger group of data than actually collected • Sampling- designing of sample survey, selection of representative sample • Probability- quantifying uncertainties varsha varde

6. History of OR • Origin: research in military operations • 1930’s: British scientists helped in solving problems of military operations, such as: • Effective use of radar, Anti-submarine warfare, civilian defence, deployment of convoy vessels • Team: Experts from various disciplines • Inter disciplinary character of OR still continues • World war II: Military operations research in US. varsha varde

7. History of OR • Post world war-II: Military continued using OR analysts • But, OR as a discipline not accepted in outside world • Reason: OR solves only military problems • Two Events helped spread to non –military establishments • Development of Simplex method in1947 • Development and usage of high speed computers • OR as a discipline came into existencein1950’s • OR: Systematic and scientific approach to problem solving varsha varde

8. Models in Operations Research • Linear programming • Transportation • Assignment • Inventory • Queuing • Project scheduling • Simulation • Decision analysis varsha varde

9. Statistical Problems 1. A market analyst wants to know the effectiveness of a new diet. 2. A pharmaceutical Co. wants to know if a new drug is superior to already existing drugs, or possible side effects. 3. How fuel efficient a certain car model is? varsha varde 9

10. Statistical Problems 4. Is there any relationship between your Grades and employment opportunities. 5. If you answer all questions on a (T,F) (or multiple choice) examination completely randomly, what are your chances of passing? 6. What is the effect of package designs on sales varsha varde 10

11. Statistical Problems 7. How to interpret polls. How many individuals you need to sample for your inferences to be acceptable? What is meant by the margin of error? 8. What is the effect of market strategy on market share? 9. How to pick the stocks to invest in? varsha varde 11

12. Course Coverage • Essential Basics Management • Data Classification & Presentation Tools • Preliminary Analysis & Interpretation of Data • Correlation Model • Regression Model • Time Series Model • Forecasting • Uncertainty and Probability • Probability Distributions • Sampling and Sampling Distributions • Estimation and Testing of Hypothesis • Chi-Square and Analysis of Variance • Decision Theory • Linear Programming varsha varde 12

13. Suggested Reading • Statistics for Management by Richard I Levin-Prentice Hall Of India –New DelhiDavid C. Howell (2003) • Quantitative Techniques for Management Decisions by U K Srivastava & Others-New Age International-New Delhi • Quantitative Methods for Business by David R Anderson &Others-Thomson Learning-New Delhi • Business Statistics by David M Levine & Others-Pearson Education-Delhi-2004 varsha varde 13

14. Quantitative Methods Essential Basics varsha varde

15. Types of Numbers • Nominal Numbers • Ordinal Numbers • Cardinal Numbers varsha varde 15

16. Nominal Numbers • Purpose: Identification of an Object • Example: House Number (10 Janpath) Telephone Number Smart Card PINumber Number on Cricket T-Shirt • No Quantitative Properties Except Equivalence: Two Different Nominal Numbers Indicate Two Different Objects varsha varde 16

17. Silent Disaster • Nominal Nos. look like normal numerals • Prime Foods CEO’s Tel No.: 23249843 • Prime Foods Ltd. Sales: Rs. 23249843 • No computer will stop you if you ask it to add nominal numbers (or multiply, divide) • But, resultant figure makes no sense • Still, this mistake is made occasionally.

18. Ordinal Numbers • Purpose: Represent Position or Ranking • Example: WTA Ranking of Sania Mirza Salary Grade Floor Number Performance Rating • No Quantitative Properties Except Order & Equivalence: Different Ordinal Numbers Indicate Different Objects in Some Kind of Relationship with Each Other varsha varde 18

19. Silent Disaster • Ordinal Nos. look like normal numerals • Sania Mirza’s weight (kg) : 53 • Sania Mirza’s WTA Ranking : 53 • You can safely add weights & divide them • No computer will stop you if you ask it to add ordinal numbers (or multiply, divide) • But, the resultant figure makes no sense • Still, this blunder is committed frequently.

20. Cardinal Numbers • Purpose: Represent Quantity • Example: Sales Turnover in Million Rs. Production in Tons Number of Employees Earning Per Share • Truly Quantitative • Follow All Mathematical Properties: Order, Equivalence, +, -, x, /. varsha varde 20

21. Interval and Ratio Scales • Interval Scale employs arbitrary zero point • Ratio Scale employs a true zero point • Only ratio scale permits statements concerning ratios of numbers in the scale; e.g 4kgs to 2 kgs is 2kgs to 1 kg • Scale of Temperature measured in Celsius is Interval Scale. • Height as measured from a table top has interval scale • Height as measured from floor has ratio scale • Apart from difference in the nature of zero point ,interval and ratio scales have same properties and both employ cardinal numbers varsha varde

22. Example varsha varde 22

23. Example varsha varde 23

24. Third place Second place First place Primary Scales of Measurement Scale NominalNumbers Assigned to Runners OrdinalRank Order of Winners IntervalPerformance Rating on a 0 to 10 Scale Ratio Time to Finish, in Seconds Finish 7 8 3 Finish 8.2 9.1 9.6 15.2 14.1 13.4

25. Primary Scales of MeasurementNominal Scale • The numbers serve only as labels or tags for identifying and classifying objects. • When used for identification, there is a strict one-to-one correspondence between the numbers and the objects. • The numbers do not reflect the amount of the characteristic possessed by the objects. • The only permissible operation on the numbers in a nominal scale is counting. • Only a limited number of statistics, all of which are based on frequency counts, are permissible, e.g., percentages, and mode.

26. Illustration of Primary Scales of Measurement Nominal Ordinal Ratio Scale Scale Scale Preference $ spent last No. Store Rankings 3 months 1. Lord & Taylor 2. Macy’s 3. Kmart 4. Rich’s 5. J.C. Penney 6. Neiman Marcus 7. Target 8. Saks Fifth Avenue 9. Sears 10.Wal-Mart IntervalScale Preference Ratings 1-7

27. Primary Scales of MeasurementOrdinal Scale • A ranking scale in which numbers are assigned to objects to indicate the relative extent to which the objects possess some characteristic. • Can determine whether an object has more or less of a characteristic than some other object, but not how much more or less. • Any series of numbers can be assigned that preserves the ordered relationships between the objects. • In addition to the counting operation allowable for nominal scale data, ordinal scales permit the use of statistics based on centiles, e.g., percentile, quartile, median.

28. Primary Scales of MeasurementInterval Scale • Numerically equal distances on the scale represent equal values in the characteristic being measured. • It permits comparison of the differences between objects. • The location of the zero point is not fixed. Both the zero point and the units of measurement are arbitrary. • Any positive linear transformation of the form y = a + bx will preserve the properties of the scale. • It is not meaningful to take ratios of scale values. • Statistical techniques that may be used include all of those that can be applied to nominal and ordinal data, and in addition the arithmetic mean, standard deviation, and other statistics commonly used in marketing research.

29. Primary Scales of MeasurementRatio Scale • Possesses all the properties of the nominal, ordinal, and interval scales. • It has an absolute zero point. • It is meaningful to compute ratios of scale values. • Only proportionate transformations of the form y = bx, where b is a positive constant, are allowed. • All statistical techniques can be applied to ratio data.

30. Primary Scales of Measurement

31. Basic Definitions Constant: A Characteristic that never changes its Value (Your Height after 20) Variable: A Characteristic that assumes different Values (Your Weight after 20) Discrete Variable: Cannot take a Value Between Any Two Values (Staff Strength) Continuous Variable: Can take a Value Between Any Two Values (P-E Ratio) varsha varde 31 31

32. Discrete Measurement Data Only certain values are possible (there are gaps between the possible values). Continuous Measurement Data Theoretically, any value within an interval is possible with a fine enough measuring device. varsha varde 32

33. Discrete data -- Gaps between possible values 0 1 2 3 4 5 6 7 Continuous data -- Theoretically, no gaps between possible values 0 1000 varsha varde 33

34. Examples: Discrete Measurement Data • Number of students late for class • Number of crimes reported in a police station • Number of times a particular word is used • Number of defectives in a lot Generally, discrete data are counts. varsha varde 34

35. Examples:Continuous Measurement Data • Cholesterol level • Height • Age • Time to complete a homework assignment Generally, continuous data come from measurements. varsha varde 35

36. Who Cares? The type(s) of data collected in a study determine the type of statistical analysis used. varsha varde 36

37. For example ... • Categorical data are commonly summarized using “percentages” (or “proportions”). • 31% of students have a passport • 2%, 33%, 39%, and 26% of the students in class are, respectively engineers, science, commerce and arts graduates varsha varde 37

38. And for example … • Measurement data are typically summarized using “averages” (or “mean • Average weight of male students of this batch is 75 kg. • Average weight of female students of this batch is 55 kg. • Average growth rate of sales of a company is 18%. varsha varde 38

39. Course Coverage • Essential Basics for Business Executives • Data Classification & Presentation Tools • Preliminary Analysis & Interpretation of Data • Correlation Model • Regression Model • Time Series Model • Forecasting • Uncertainty and Probability • Sampling Techniques • Estimation and Testing of Hypothesis varsha varde 39

40. Quantitative Methods Data Classification and Presentation Tools varsha varde

41. Data Classification • First Step: Organize Data Systematically • Arrange the Data According to a Common Characteristic Possessed by All Items • Methods: Array Frequency Array Frequency Distribution varsha varde 41

42. Example: Number of Sales Orders Booked by 50 Sales Execs April 2006 varsha varde 42

43. Array 0, 0, 0, 0, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 11, 11, 11, 12, 14, 15, 16, 17, 19, 21, 24, 28, 30, 34, 43 Array: Arrangement of Data in Order of Magnitude varsha varde 43

44. Frequency Array A Table Showing the Number of Times Each Value Occurs varsha varde 44

45. Frequency Array varsha varde 45

46. Frequency Array varsha varde 46 46

47. Frequency Distribution A Table Showing the Number of Times Each Cluster of Values Occurs varsha varde 47

48. Constructing Frequency Distribution • Find Maximum & Minimum Values in Data. • Make Sub-Intervals to Cover Entire Range • They are Called the ‘Class Intervals’. • Class Intervals Need Not Be of Equal Length. But, it is Useful if They Are. • Note the Number of Observation that Belong to Each Class Interval. • They are Called the ‘Frequencies’. varsha varde 48

49. Frequency Distribution varsha varde 49

50. In This Example • What is the Variable? Sales Executives or Sales Orders? • Is it Nominal, Ordinal or Cardinal? • Is it Discrete or Continuous? • What are the frequencies (sometimes called as frequency values or score)? varsha varde 50