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LESSON 2 Business Statistics

This lesson covers the basics of business statistics, including interpreting statistics and probability distributions, as well as evaluating statistics for decision making. Topics include customer demand estimates and uncertainty in the supply chain.

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LESSON 2 Business Statistics

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  1. LESSON 2Business Statistics 29 August 2014

  2. Lesson Objectives Upon completion of this lesson, you should be able to: • Interpret business statistics and related graphical representations • Interpret probability distributions and graphical representations • Evaluate business statistics for a given scenario

  3. Lesson Topics This lesson will cover the following topics: • Business Statistics Introduction • Probability • Customer Demand by Point Estimates • Uncertainty in the Supply Chain • Data-Based Decision Making

  4. What’s In It For Me? Use of business statistics enables you quantitatively monitor your contractors’ manufacturing and supply chain management decisions and performance

  5. Introduction How does the use of business statistics help you to evaluate and support your contractors?

  6. Business Statistics Introduction Lesson Topics: Business Statistics Introduction Probability Customer Demand by Point Estimates Uncertainty in the Supply Chain Data-Based Decision Making

  7. Business Statistics Introduction • Monitoring contractor performance requires you to predict how likely a contractor is to meet contract requirements • Business statistics will help you to make this determination, thereby alerting you to potential risk

  8. Notations Definitions of common notations used in business statistics: • Mu = µ • Sigma = σ • Sigma squared = σ2

  9. Descriptive Statistics ~ x x

  10. Descriptive Statistics (cont.) • Describe the body of data • Provide a full picture of the data • Avoid limiting descriptive measures, which could give the audience only part of the picture • Use at least one measure of dispersion and at least one measure of central tendency

  11. Location of Data • Summarizes a set of values into a single number • Mean: Average of all the values • Median: Middle of an ordered list of the values • Mode: Occurs most often • Example: • Data Set: 1, 1, 1, 4, 5, 6, 6, 6, 6 • Mean: 4 • Median: 5 • Mode: 6

  12. Dispersion Dispersion is the variability from the expected value Example: A = (25, 25, 25, 25) yields a mean of 25 B = (1, 1, 1, 97) also yields a mean of 25 However, set B displays significantly more dispersion than set A.

  13. Measures of Dispersion

  14. Range 1. Max = 30 2. Min = -29 3. Range = 30--29 = 59 The rangeis the difference between the highest and lowest valuesRange = 30--29 = 59

  15. Variance m = (30+-23+17+12+30+-18+-24+-29+18+8 ) / 10 m = 21 / 10 m = 2.1 1. Compute the mean. The mean is denoted by m m = 2.1

  16. Variance (cont.) 2. Compute the squared distance from the mean for all data points Example:d5= p5 – m = 30 – 2.1 = 27.9 d52 = (27.9)2 = 778.41 1. Compute the mean. The mean is denoted by m m = 2.1 Distance From Mean2 d52 d12 d12 d32 d92 d42 d102 d62 d82 d72 d22 3. The variance is the average of the squared distancesIt is denoted by s2 s2 = 484.69 s2 = (778.41 + 630.01 + 222.01 + 98.01 + 778.41 + 404.01 + 681.21 + 967.21 + 252.81 + 34.81) / 10 s2 = 4,846.90 / 10 s2 = 484.69

  17. Standard Deviation Standard deviation is the square root of the variance (s) s2 =  484.69 s = 22.01 d52 d12 d12 d32 d92 d42 d102 d62 d82 d72 d22

  18. Coefficient of Variation • The coefficient of variation is the standard deviation divided by the mean • = 22.01 • = 2.1 • Cv= s/m =22.01/2.1 = 10.48 d52 d12 d12 d32 d92 d42 d102 d62 d82 d72 d22

  19. Measures of Dispersion Using Excel =VAR.P(B2:B11) Address of the range containing the data • Excel offers both VAR.P and VAR.S • VAR.P calculates variance based on the entire population • VAR.S estimates variance based on a sample

  20. What is the average of a data set? Question and Answer • Median • Mode • Dispersion • Mean

  21. What is the middle data point in a data set? Question and Answer • Median • Mode • Dispersion • Mean

  22. The variability from the expected value is__________. Question and Answer • Median • Mode • Dispersion • Mean

  23. To provide a full picture of the data use _________________. Question and Answer • Central Tendency • Descriptive statistics • Location • Variability

  24. Probability Lesson Topics: Business Statistics Introduction Probability Customer Demand by Point Estimates Uncertainty in the Supply Chain Data-Based Decision Making

  25. Probability • Probability data enables you to: • Forecast and plan • Anticipate customer needs • Mitigate risk

  26. Probability (cont.)

  27. Notation The probability of an outcome xis denoted as p(x)

  28. Observations Probabilities are always between 0 and 1

  29. Probability Distributions (1 of 3) • Probability distributions describe the probabilities of all possible outcomes for an uncertain event Probability Distribution for a Fair Coin with Two Surfaces Probability Distribution for a Fair Die with Six Surfaces

  30. Probability Distributions (2 of 3) Probabilities for a Fair Die with Six Surfaces

  31. Probability Distributions (3 of 3) Probability Distribution for Two Fair Dice with Six Surfaces

  32. What is the probability of flipping a head with a fair coin? Question and Answer • 1/1 • 1/2 • 1/3 • 1/4

  33. What is the probability of rolling a 3 with a fair die with six surfaces? Question and Answer • 1/36 • 3/6 • 3/36 • 1/6

  34. What is the probability of rolling a 7 with two fair dice with six surfaces? Question and Answer • 3/16 • 1/2 • 6/36 • 5/7

  35. Two Types of Probability Distributions Probability distributions describe the probabilities of all possible outcomes for an uncertain event • Discrete • Integral outcomes (e.g., number of customers, number of defects) • Categorical outcomes (e.g., heads or tails, success or failure) • Continuous • Outcomes can assume any value (e.g., fuel consumption, distance, weight)

  36. Example: Probability Distribution Chairs & Moore is analyzing defect rates for a manufacturing center over the course of the past month. Some chairs produced had no defects, but some units had several defects. You obtained the following results for the 188 chairs completed Probability Distribution for Number of Defects per Chair Produced

  37. Example: Probability Distribution (cont.) • What is the probability that the next unit produced will be free of defects? Probability (0 defects) = 101/188 = ~53.7% Probability Distribution for Number of Defects per Chair Produced

  38. Types of Probability Distributions

  39. Graphical Representations of Probability Distributions Range Considered26 ≤ X < 27

  40. Graphing Probability Distribution Frequency histogramsindicate the number of times an occurrence takes place Probability Distribution for Number of Defects per Chair Produced The height of each bar indicates how many units had a particular number of defects

  41. Graphing Probability Distribution (cont.) Probability distribution is the same as a frequency histogram except the Y-axis is expressed as a percentage Probability Distribution for Number of Defects per Chair Produced Frequency Histogram Probability Distribution Y-axis of probability distribution expressed as percentage of total occurrences Y-axis of frequency histogram expressed as number of occurrences

  42. The probabilities of all possible outcomes for an uncertain event describes __________________. Question and Answer • Central tendencies • Probability distributions • Measures of dispersion • Descriptive statistics

  43. Which of the following contractors’ data demonstrates less risk? Question and Answer

  44. Cumulative Probability Distributions Cumulative probability distributions represent the total probability for all values up to and including a given value Probability Distribution for a Fair Die with Six Surfaces Cumulative probability distribution will never exceed 1, which is equal to 100% Probability Distribution for Two Fair Dice with Six Surfaces

  45. Discrete vs. Continuous Cumulative Probability Distributions

  46. Example: Cumulative Probability Large Group Scenario: • Refer to Module 5, Lesson 2, Scenario 1CME130_M5_L2_S1_Scenario_FINAL.docx • Read the directions in the scenario • Complete the activity as a class

  47. Example: Cumulative Probability (cont.) Results: 418 units of on-hand inventory are needed to meet a 99.5% service level guarantee 418 99.5%

  48. Skew Shape and Mean, Median, and Mode Consider the following data set: 4 ; 5 ; 6 ; 6 ; 6 ; 7 ; 7 ; 7 ; 7 ; 7 ; 7 ; 8 ; 8 ; 8 ; 9 ; 10 Consider the following data set: 4 ; 5 ; 6 ; 6 ; 6 ; 7 ; 7 ; 7 ; 7 ; 8 Consider the following data set: 6 ; 7 ; 7 ; 7 ; 7 ; 8 ; 8 ; 8 ; 9 ; 10 Notice the mean, median, and mode are all the same. The mean is 7, the median is 7, and the mode is 7 Notice the mean is less than the median, and they are both less than the mode. The mean is 6.3, the median is 6.5, and the mode is 7 Notice the mean is the largest, while the mode is the smallest. The mean is 7.7, the median is 7.5, and the mode is 7 Distribution is symmetric and bell shaped. Mean, median, and mode are the highest point Negatively skewed or skewed left, meaning the left tail is longer Positively skewed or skewed right, meaning the right tail is longer

  49. Cumulative probability distributions represent the what, up to and including a given value? Question and Answer • Total probability for all values • Partial probability for all values • Total probability for the mean • Partial probability for the median

  50. Discussion Opportunity • What information can you interpret from the following image? • How can the information provided help you make better supply management decisions?

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