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

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• Percentiles are values based on rankings within a sorted list. The most common percentile is the median (50th percentile) which represents the middle value in a sorted list of values. For a normally distributed data set, this is identical to the mean (average) of all values, but if the data is skewed, the median may provide a more accurate description of the average (for example median home price is tracked rather than average home price which may be distorted by a few expensive home sales). The 0th percentile represents the smallest value and the 100th percentile represents the largest value.
• Lesson03

1. 1. IBS Statistics<br />Year 1<br />n.ding@pl.hanze.nl<br />I.007<br />
2. 2. What we are going to learn?<br />Review<br /><ul><li>Chapter 3: Dispersion
3. 3. Range
4. 4. Variance (SD2)
5. 5. Standard Deviation (SD)
6. 6. Coefficient of variation (CV)
7. 7. Chapter 4: Displaying and exploring data
8. 8. Dotplot
9. 9. Stem-leaf
10. 10. Boxplot
11. 11. Skewness</li></li></ul><li>Review<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Discrete counting or Continuous measuring<br /><ul><li>Age
12. 12. Sales volume
13. 13. Weight
14. 14. Temperature
15. 15. Salary
16. 16. Class size
17. 17. Height
18. 18. Shoe size (NL)</li></li></ul><li>Review<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Constructing Frequency Distribution: Quantitative Data<br />45 observations<br />i= 88.33<br />571- 41<br />25 = 32, 26 = 64, suggests 6 classes<br />6<br />><br />Use interval of 100<br />P46. N.30 Ch.2<br />
19. 19. Review<br />Class interval = 100<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />0<br />relative<br />P46. N.30 Ch.2<br />
20. 20. Review<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Central Tendency : Mean, Mode, Median<br />Mean: Average<br />Median: Midpoint<br />Mode: Most Frequency<br />SCCoast, an Internet provider in the Southeast, developed the following frequency distribution on the age of Internet users. <br />Describe the central tendency:<br />X = 2410 / 60 = 40.17 (years)<br />Mode = 45 (years)<br />Median = ? (years)<br />P87 N.60 Ch.3<br />
21. 21. Review<br />Value:40 50<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Location: 28 48<br />Step 1: Define the location of the median<br />Step 2: Calculate the median<br />M<br />Lm=(60+1)/2=30.5<br />30.5-28<br />48-28<br />M-40<br />50-40<br />30.5<br />=<br />Median= 41.25<br />P87 N.60 Ch.3<br />
22. 22. Chapter 3 Dispersion<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Range<br />Variance (SD2) and Standard Deviation (SD)<br />Dispersion<br />Interquartile Range<br />Coefficient of variation (CV)<br />
23. 23. Chapter 3 Dispersion<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Dispersion: <br />Mean is not reliable<br /><ul><li>tells us about the spread of the data.
24. 24. Help us to compare the spread in two or more distributions.</li></li></ul><li>Range<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Range:<br />is the difference between the largest and the smallest value in a data set. <br />Example:<br />To find the range in 3,5,7,3,11<br />Range = 11-3 = 8<br />
25. 25. Variance<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Population Variance:<br /><ul><li>is the mean of the squared difference between each value and the mean.
26. 26. overcomes the weakness of the range by using all the values in the population. </li></ul>Sample Variance:<br />
27. 27. Variance<br />Review<br />Chapter 3: Dispersion<br /><ul><li>Range
28. 28. Variance (SD2)
29. 29. Standard Deviation (SD)
30. 30. Coefficient of variation (CV)</li></ul>Chapter 4: Displaying and exploring data<br /><ul><li>Dotplot
31. 31. Stem-leaf
32. 32. Boxplot
33. 33. Skewness</li></ul>Population Variance:<br />Step 2: Find the difference between each observation and the mean<br />Step 1: Get the mean<br />Step 3: Square the difference and sum up<br />Step 4: Divided by N<br />
34. 34. Standard Deviation<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Population Standard Deviation:<br />is the square root of the population variance. <br />Sample Standard Deviation:<br />is the square root of the sample variance. <br />
35. 35. Standard Deviation<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Example:<br />The hourly wages earned by a sample of five students are:<br />€7, €5, €11, €8, €6.<br />Find the variance and standard deviation.<br />Step 1: Get the mean<br />Step 2: Sum up the squared differences<br />Step 3: Divided by N-1<br />s = €2.30<br />Step 4: Square root it<br />The variance is €5.30; <br />the standard deviation is €2.30.<br />
36. 36. Standard Deviation<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Compare<br />Schiphol<br />Utrecht<br />20 40 50 60 80<br />20 49 50 51 80<br /><ul><li>The number of coffee sales in Utrecht Starbucks is more closely clustered around the mean of 50 than for the sales number in Schiphol</li></ul>Starbucks. <br />
37. 37. Standard Deviation of Grouped Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Step 2: Use f * (M-Xmean)2<br />Step 1: Find the Midpoint<br />Step 3: Sum up<br />Step 4: Divided by N-1<br />7098<br />60-1<br />7098<br />60-1<br />= 10.97<br />Step 5: Square root it<br />P87 N.60 Ch.3<br />
38. 38. Coefficient of Variation<br />This is the ratio of the standard deviation to the mean:<br />The coefficient of variation describes the magnitude sample values and the variation within them. <br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />The following times were recorded by the quarter-mile and mile runners of a university <br /> track team (times are in minutes).<br />Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99<br /> Mile Times: 4.52 4.35 4.60 4.70 4.50<br />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.<br />We can compare the dispersion with the coefficient of variation because they have different “magnitudes”. <br />
39. 39. Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />The following times were recorded by the quarter-mile and mile runners of a university <br /> track team (times are in minutes).<br />Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99<br /> Mile Times: 4.52 4.35 4.60 4.70 4.50<br />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.<br />We can compare the dispersion with the coefficient of variation because they have different “magnitudes”. <br />Coefficient of variation of Q-Mile Times is: 0.05639/0.966=0.05837==>6%<br />Coefficient of variation of Mile Times is: 0.12954/4.534=0.02857==>3%<br />No, the mile-time team showed more consistent times. <br />
40. 40. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Dot plots:<br />
41. 41. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Stem-and-Leaf Displays:<br />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. <br />Leaf<br />Stem<br />
42. 42. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br /><ul><li>Range
43. 43. Variance (SD2)
44. 44. Standard Deviation (SD)
45. 45. Coefficient of variation (CV)</li></ul>Chapter 4: Displaying and exploring data<br /><ul><li>Dotplot
46. 46. Stem-leaf
47. 47. Boxplot
48. 48. Skewness</li></ul>Stem-and-Leaf Displays:<br />
49. 49. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Quartiles, Deciles, and Percentiles<br />Alternative ways of describing spread of data include determining the<br />location of values that divide a set of observations into equal parts. <br />
50. 50. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Quartiles, Deciles, and Percentiles<br />
51. 51. Chapter 4 Displaying and Exploring Data<br />Raw Percentile <br />Score Frequency Frequency Rank<br />95 1 25 100<br />93 1 24 96<br />88 2 23 92<br />85 3 21 84<br />79 1 18 72<br />75 4 17 68<br />70 6 13 52<br />65 2 7 28<br />62 1 5 20<br />58 1 4 16<br />54 2 3 12<br />50 1 1 4<br /> N = 25<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Quartiles,Deciles, and Percentiles<br />
52. 52. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Quartiles, Deciles, and Percentiles<br />Example:<br />43<br />61<br />91<br />75<br />101<br />104<br />The first quartile is ?<br />
53. 53. Chapter 4 Displaying and Exploring Data<br />L25 = (n+1) = (6+1) =1.75 <br />Step 2:<br />P<br />100<br />25<br />100<br />P1<br />P2<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Quartiles, Deciles, and Percentiles<br />Organize the data from lowest to largest value<br />Step 1:<br />43<br />61<br />91<br />75<br />101<br />104<br />P1 P2 P3 P4 P5 P6<br />P1.75<br />Draw two lines<br />Step 3:<br />61-43 = 18<br />43<br />61<br />0.75<br />
54. 54. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Quartiles, Deciles, and Percentiles<br />Draw two lines<br />Step 3:<br />43+13.5 = 56.5<br />43<br />61<br />61-43 = 18<br />0.75<br />* 18 =<br />13.5<br />P1<br />P2<br />The first quartile is 56.5. <br />
55. 55. Exercise<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Listed below, ordered from smallest to largest, are the number of visits last week. <br />a. Determine the median number of calls. <br />The median is 58. <br />b. Determine the first and third quartiles.<br />Q1 = 51.25 Q3 = 66.00<br />P110. N.14 Ch.4<br />
56. 56. Exercise<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Listed below, ordered from smallest to largest, are the number of visits last week. <br />c. Determine the first decile and the ninth decile.<br />D1 = 45.30 D9 = 76.40<br />d. Determine the 33rd percentile.<br />P33 = 53.53<br />P110. N.14 Ch.4<br />
57. 57. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Box Plots<br />A graphical display, based on quartiles to visualize a set of data. <br />minimum<br />Q1<br />Median<br />Q3<br />maximum<br />
58. 58. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Box Plots<br />minimum<br />Q1<br />Median<br />Q3<br />maximum<br />
59. 59. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Box Plots & Cumulative Frequency Distribution<br />minimum<br />Q1<br />Median<br />Q3<br />maximum<br />
60. 60. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />minimum<br />Q1<br />Median<br />Q3<br />maximum<br />
61. 61. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />skewed<br />Skewness:<br />Another characteristic of a set of data is the shape. <br /><ul><li>symmetric,
62. 62. positively skewed,
63. 63. negatively skewed,
64. 64. bimodal.</li></li></ul><li>Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Zero skewness<br />mode=median=mean<br />
65. 65. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />positive skewness<br />Mode median mean<br />
66. 66. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />negative skewness<br />Mode median mean<br />
67. 67. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />
68. 68. Chapter 4 Displaying and Exploring Data<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />Skewness:<br /><ul><li>symmetric,
69. 69. positively skewed,
70. 70. negatively skewed,
71. 71. bimodal.</li></li></ul><li>Exercise<br />Review<br />Chapter 3: Dispersion<br />Range<br />Variance (SD2)<br />Standard Deviation (SD)<br />Coefficient of variation (CV)<br />Chapter 4: Displaying and exploring data<br />Dotplot<br />Stem-leaf<br />Boxplot<br />Skewness<br />A sample of 28 time shares in the Orlando, Florida, area revealed the following daily charges for a one-bedroom suite. For convenience the data are ordered from smallest to largest. Construct a box plot to represent the data. Comment on the distribution. Be sure to identify the first and third quartiles and the median. <br /><ul><li>The median is \$253.
72. 72. About 25% of the semi-private rooms are less than \$214 and 25% above \$304.
73. 73. The distribution is negatively skewed. </li></ul>P113. N.18 Ch.4<br />
74. 74. What we have learnttoday?<br /><ul><li>Review
75. 75. Chapter 3: Dispersion
76. 76. Range
77. 77. Variance (SD2)
78. 78. Standard Deviation (SD)
79. 79. Coefficient of variation (CV)
80. 80. Chapter 4: Displaying and exploring data
81. 81. Dotplot
82. 82. Stem-leaf
83. 83. Boxplot
84. 84. Skewness</li></li></ul><li>