Statistics for International Business School, Hanze University of Applied Science, Groningen, The Netherlands

1. IBS Statistics Year 1 n.ding@pl.hanze.nl I.007

3. Range

4. Variance (SD2)

5. Standard Deviation (SD)

6. Coefficient of variation (CV)

7. Chapter 4: Displaying and exploring data

8. Dotplot

9. Stem-leaf

10. Boxplot

12. Sales volume

13. Weight

14. Temperature

15. Salary

16. Class size

17. Height

19. Review Class interval = 100 Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness 0 relative P46. N.30 Ch.2

20. Review Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Central Tendency : Mean, Mode, Median Mean: Average Median: Midpoint Mode: Most Frequency SCCoast, an Internet provider in the Southeast, developed the following frequency distribution on the age of Internet users. Describe the central tendency: X = 2410 / 60 = 40.17 (years) Mode = 45 (years) Median = ? (years) P87 N.60 Ch.3

21. Review Value:40 50 Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Location: 28 48 Step 1: Define the location of the median Step 2: Calculate the median M Lm=(60+1)/2=30.5 30.5-28 48-28 M-40 50-40 30.5 = Median= 41.25 P87 N.60 Ch.3

22. Chapter 3 Dispersion Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Range Variance (SD2) and Standard Deviation (SD) Dispersion Interquartile Range Coefficient of variation (CV)

26. overcomes the weakness of the range by using all the values in the population. Sample Variance:

28. Variance (SD2)

29. Standard Deviation (SD)

31. Stem-leaf

32. Boxplot

33. SkewnessPopulation Variance: Step 2: Find the difference between each observation and the mean Step 1: Get the mean Step 3: Square the difference and sum up Step 4: Divided by N

34. Standard Deviation Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Population Standard Deviation: is the square root of the population variance. Sample Standard Deviation: is the square root of the sample variance.

35. Standard Deviation Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Example: The hourly wages earned by a sample of five students are: €7, €5, €11, €8, €6. Find the variance and standard deviation. Step 1: Get the mean Step 2: Sum up the squared differences Step 3: Divided by N-1 s = €2.30 Step 4: Square root it The variance is €5.30; the standard deviation is €2.30.

37. Standard Deviation of Grouped Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Step 2: Use f * (M-Xmean)2 Step 1: Find the Midpoint Step 3: Sum up Step 4: Divided by N-1 7098 60-1 7098 60-1 = 10.97 Step 5: Square root it P87 N.60 Ch.3

38. Coefficient of Variation This is the ratio of the standard deviation to the mean: The coefficient of variation describes the magnitude sample values and the variation within them. Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness The following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes). Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99 Mile Times: 4.52 4.35 4.60 4.70 4.50 After viewing this sample of running times, one of the coaches commented that the quarter milers turned in the more consistent times. Calculate the appropriate measure to check this and comment on the coach’s statement. We can compare the dispersion with the coefficient of variation because they have different “magnitudes”.

39. Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness The following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes). Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99 Mile Times: 4.52 4.35 4.60 4.70 4.50 After viewing this sample of running times, one of the coaches commented that the quarter milers turned in the more consistent times. Calculate the appropriate measure to check this and comment on the coach’s statement. We can compare the dispersion with the coefficient of variation because they have different “magnitudes”. Coefficient of variation of Q-Mile Times is: 0.05639/0.966=0.05837==>6% Coefficient of variation of Mile Times is: 0.12954/4.534=0.02857==>3% No, the mile-time team showed more consistent times.

40. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Dot plots:

41. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Stem-and-Leaf Displays: Each numerical value is divided into two parts. The leading digit(s) becomes the stem and the trailing digit the leaf. The stems are located along the vertical axis, and the leaf values are stacked against each other along the horizontal axis. Leaf Stem

43. Variance (SD2)

44. Standard Deviation (SD)

46. Stem-leaf

47. Boxplot

48. SkewnessStem-and-Leaf Displays:

49. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Quartiles, Deciles, and Percentiles Alternative ways of describing spread of data include determining the location of values that divide a set of observations into equal parts.

50. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Quartiles, Deciles, and Percentiles

51. Chapter 4 Displaying and Exploring Data Raw Percentile Score Frequency Frequency Rank 95 1 25 100 93 1 24 96 88 2 23 92 85 3 21 84 79 1 18 72 75 4 17 68 70 6 13 52 65 2 7 28 62 1 5 20 58 1 4 16 54 2 3 12 50 1 1 4 N = 25 Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Quartiles,Deciles, and Percentiles

52. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Quartiles, Deciles, and Percentiles Example: 43 61 91 75 101 104 The first quartile is ?

53. Chapter 4 Displaying and Exploring Data L25 = (n+1) = (6+1) =1.75 Step 2: P 100 25 100 P1 P2 Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Quartiles, Deciles, and Percentiles Organize the data from lowest to largest value Step 1: 43 61 91 75 101 104 P1 P2 P3 P4 P5 P6 P1.75 Draw two lines Step 3: 61-43 = 18 43 61 0.75

54. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Quartiles, Deciles, and Percentiles Draw two lines Step 3: 43+13.5 = 56.5 43 61 61-43 = 18 0.75 * 18 = 13.5 P1 P2 The first quartile is 56.5.

55. Exercise Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Listed below, ordered from smallest to largest, are the number of visits last week. a. Determine the median number of calls. The median is 58. b. Determine the first and third quartiles. Q1 = 51.25 Q3 = 66.00 P110. N.14 Ch.4

56. Exercise Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Listed below, ordered from smallest to largest, are the number of visits last week. c. Determine the first decile and the ninth decile. D1 = 45.30 D9 = 76.40 d. Determine the 33rd percentile. P33 = 53.53 P110. N.14 Ch.4

57. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Box Plots A graphical display, based on quartiles to visualize a set of data. minimum Q1 Median Q3 maximum

58. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Box Plots minimum Q1 Median Q3 maximum

59. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness Box Plots & Cumulative Frequency Distribution minimum Q1 Median Q3 maximum

60. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness minimum Q1 Median Q3 maximum

62. positively skewed,

63. negatively skewed,

65. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness positive skewness Mode median mean

66. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness negative skewness Mode median mean

67. Chapter 4 Displaying and Exploring Data Review Chapter 3: Dispersion Range Variance (SD2) Standard Deviation (SD) Coefficient of variation (CV) Chapter 4: Displaying and exploring data Dotplot Stem-leaf Boxplot Skewness

69. positively skewed,

70. negatively skewed,

72. About 25% of the semi-private rooms are less than $214 and 25% above $304.

73. The distribution is negatively skewed. P113. N.18 Ch.4

75. Chapter 3: Dispersion

76. Range

77. Variance (SD2)

78. Standard Deviation (SD)

79. Coefficient of variation (CV)

80. Chapter 4: Displaying and exploring data

81. Dotplot

82. Stem-leaf

83. Boxplot