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# Lesson 3

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Introductory of Business statistics
Hanze University of Applied Sciences

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### Lesson 3

1. 1. Hanze University of Applied Science GroningenNing Ding, PhDLecturer of International BusinessSchool (IBS)n.ding@pl.hanze.nl
2. 2. What we are going to learn?• 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
3. 3. Review a bReviewChapter 3: Discrete counting Continuous measuringDispersion–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying and 1.Age 5. Salaryexploring data–Dotplot–Stem-leaf 2.Sales volume 6. Class size–Boxplot–Skewness 3. Temperature 7. Height 4. Weight 8. Shoe size (NL)
4. 4. Review Constructing Frequency Distribution: Quantitative Data a. 4 b.5 c.6 d.70 25 = 32, 26 = 64, suggests 6 classes Use interval of 100 a. 80 b.100 c.120 d.150i> 571- 41 = 88.33 6 P46. N.30 Ch.2
5. 5. Review0 Cumulative Class interval = 100 relative relative P46. N.30 Ch.2
6. 6. Central Tendency : Mean, Mode, MedianMean: Average 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) P87 N.60 Ch.3
7. 7. Review Central Tendency : Mean, Mode, MedianMean: Average 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: Mode = 45 (years) P87 N.60 Ch.3
8. 8. Review Central Tendency : Mean, Mode, Median Mean: Average Mode: Most Frequency Median: Midpoint SCCoast, an Internet provider in the Southeast, developed the following frequency distribution on the age of Internet users. Describe the central tendency:a.40.25b.41.25c.30.50d.37.50 Median = ? (years) P87 N.60 Ch.3
9. 9. ReviewStep 1: Define the location of the median Step 2: Calculate the median M Lm=(60+1)/2=30.5 Value:40 50 Location: 28 48 30.5 30.5-28 M-40 = 48-28 50-40 Median= 41.25 P87 N.60 Ch.3
10. 10. DispersionReview RangeChapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation (SD) Variance (SD2) and Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying and Interquartile Rangeexploring data–Dotplot–Stem-leaf–Boxplot Coefficient of variation (CV)–Skewness
11. 11. DispersionReview – tells us about the spread of the data.Chapter 3: – Help us to compare the spread in two or moreDispersion distributions.–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness
12. 12. Dispersion: RangeReview Range:Chapter 3: is the difference between the largest andDispersion–Range the smallest value in a data set.–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV) Example:Chapter 4:Displaying and To find the range in 3,5,7,3,11exploring data–Dotplot–Stem-leaf Range = 11-3 = 8–Boxplot–Skewness
13. 13. Dispersion: VarianceReview Population Variance: • is the mean of the squared difference between eachChapter 3:Dispersion value and the mean.–Range • overcomes the weakness of the range by using all the–Variance (SD2)–Standard Deviation values in the population. (SD)–Coefficient of variation (CV) Σ(X - μ) 2 σ2 =Chapter 4: NDisplaying andexploring data–Dotplot–Stem-leaf Sample Variance:–Boxplot Σ(X - X) 2–Skewness s2 = n -1
14. 14. EXAMPLE – Variance Variance Dispersion: and Standard Deviation Population Variance: Σ(X - μ) 2 σ2 =Review N The number of traffic citations issued during the last five months inChapter 3:Dispersion Beaufort County, South Carolina, is 38, 26, 13, 41, and 22. What–Range is the population variance?–Variance (SD2)–Standard Deviation Step 2: Find the difference between each observation and the mean (SD)–Coefficient of variation (CV)Chapter 4:Displaying and Step 1: Get the meanexploring data–Dotplot–Stem-leaf–Boxplot–Skewness Step 3: Square the difference and sum up Step 4: Divided by N 27
15. 15. Dispersion: Standard DeviationReviewChapter 3:Dispersion Population Standard Deviation:–Range–Variance (SD2) is the square root of the population variance.–Standard Deviation σ= σ2 (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot Sample Standard Deviation:–Stem-leaf–Boxplot is the square root of the sample variance.–Skewness s = s2
16. 16. Dispersion: Standard Deviation Example:Review The hourly wages earned by a sample of five students are: €7, €5, €11, €8, €6.Chapter 3:Dispersion Find the variance and standard deviation.–Range Step 1: Get the mean ΣX 37–Variance (SD2) X= = = 7.40–Standard Deviation (SD) n 5 2 Σ(X - X ) 2 2–Coefficient of Step 2: Sum up the (7 - 7.4) + ... + (6 - 7.4) variation (CV) squared differences s2 = = n -1 5 -1Chapter 4: 21.2Displaying and = = 5.30exploring data–Dotplot Step 3: Divided by N-1 5 -1–Stem-leaf–Boxplot–Skewness Step 4: Square root it s = €2.30 The variance is €5.30; the standard deviation is €2.30.
17. 17. Dispersion: Standard DeviationReviewChapter 3:Dispersion Compare–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of 20 40 50 60 80 20 49 50 51 80 variation (CV)Chapter 4:Displaying and Step 1: Get the meanexploring data–Dotplot–Stem-leaf Step 2: Sum up the–Boxplot squared differences–Skewness Step 3: Divided by N-1 Step 4: Square root it
18. 18. Dispersion: Standard DeviationReviewChapter 3:Dispersion Compare–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of 20 40 50 60 80 20 49 50 51 80 variation (CV)Chapter 4:Displaying andexploring data •The sales of–Dotplot–Stem-leaf MANGO is more–Boxplot–Skewness closely clustered around the mean of 50 than the sales of ZARA.
19. 19. Dispersion: Standard DeviationReviewChapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness The standard deviation decreases because the new value 20 is very close to the mean 20.36.
20. 20. Dispersion: Standard DeviationStep 1: Step 3: Use f * (Mid-Mean)2Find the MidpointStep 2:Calculate the Mean P87 N.60 Ch.3
21. 21. Dispersion: Standard DeviationStep 4:Calculate the VarianceStep 5:Calculate the Standard Deviation P87 N.60 Ch.3
22. 22. Dispersion: Coefficient of VariationReview Coefficient of Variation:Chapter 3: describes the magnitude sample values and the variation withinDispersion them.–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV) The following times were recorded by the quarter-mile and mile runners of aChapter 4: university track team (times are in minutes).Displaying andexploring data Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99–Dotplot–Stem-leaf Mile Times: 4.52 4.35 4.60 4.70 4.50–Boxplot After viewing this sample of running times, one of the coaches commented that–Skewness 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”.
23. 23. Dispersion: Coefficient of Variation 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
24. 24. Dispersion: Coefficient of Variation The following times were recorded by the quarter-mile and mile runners of aReview university track team (times are in minutes).Chapter 3: Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99Dispersion Mile Times: 4.52 4.35 4.60 4.70 4.50–Range–Variance (SD2) After viewing this sample of running times, one of the coaches commented that–Standard Deviation the quarter milers turned in the more consistent times. Calculate the appropriate (SD) measure to check this and comment on the coach’s statement.–Coefficient of variation (CV) We can compare the dispersion with the coefficient of variation because they have different “magnitudes”.Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness No, the mile-time team showed more consistent times.
25. 25. Displaying and Exploring DataReview Dot plots:Chapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness
26. 26. Displaying and Exploring DataReview Stem-and-Leaf Displays:Chapter 3: Each numerical value is divided into two parts. The leadingDispersion–Range digit(s) becomes the stem and the trailing digit the leaf. The–Variance (SD2) stems are located along the vertical axis, and the leaf values are–Standard Deviation (SD) stacked against each other along the horizontal axis.–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness Stem
27. 27. Displaying and Exploring Data Stem-and-Leaf Displays:ReviewChapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness
28. 28. Displaying and Exploring DataReview Quartiles, Deciles, and PercentilesChapter 3: Alternative ways of describing spread of data include determiningDispersion the location of values that divide a set of observations into equal–Range parts.–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness
29. 29. Displaying and Exploring DataReview Quartiles, Deciles, and PercentilesChapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness
30. 30. Displaying and Exploring DataReview Quartiles, Deciles, and PercentilesChapter 3:Dispersion Raw Percentile–Range Score Frequency Frequency Rank–Variance (SD2)–Standard Deviation (SD) 95 1 25 100–Coefficient of 93 1 24 96 variation (CV) 88 2 23 92Chapter 4: 85 3 21 84Displaying andexploring data 79 1 18 72–Dotplot 75 4 17 68–Stem-leaf–Boxplot 70 6 13 52–Skewness 65 2 7 28 62 1 5 20 58 1 4 16 54 2 3 12 50 1 1 4 N = 25
31. 31. Displaying and Exploring DataReview Quartiles, Deciles, and PercentilesChapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV) Example:Chapter 4:Displaying and 101 43 75 61 91 104exploring data–Dotplot–Stem-leaf–Boxplot–Skewness The first quartile is ?
32. 32. Displaying and Exploring DataReviewChapter 3: Step 1: Organize the data from lowest to largest valueDispersion–Range 101 43 75 61 91 104–Variance (SD2)–Standard Deviation P1 P2 P3 P4 P5 P6 (SD)–Coefficient of variation (CV) Step 2: P1.75Chapter 4:Displaying andexploring data Step 3: Draw two lines–Dotplot–Stem-leaf–Boxplot–Skewness 43 61-43 = 18 61 P1 0.75 P2
33. 33. Displaying and Exploring DataReviewChapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation Step 3: Draw two lines (SD)–Coefficient of variation (CV) 43+13.5 = 56.5Chapter 4:Displaying and 43 61-43 = 18 61exploring data–Dotplot–Stem-leaf–Boxplot P1 0.75 * 18 = 13.5 P2–Skewness The first quartile is 56.5.
34. 34. Displaying and Exploring Data Listed below, ordered from smallest to largest, are the number of visits last week. a. Determine the median number of calls. a. 57median is 58. The b.58 c.59 d.56 b. Determine the first and third quartiles. Q1 = 51.25 Q3 = 66.00 a. 50.25 b.51.25 c.60.00 d.62.25 e.63.00 f. 66.00 P110. N.14 Ch.4
35. 35. Displaying and Exploring Data 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
36. 36. Displaying and Exploring DataReview Box Plots A graphical display, based on quartiles to visualize a set of data.Chapter 3:Dispersion–Range minimum Q1 Median Q3 maximum–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness
37. 37. Displaying and Exploring DataReview Box Plots A graphical display, based on quartiles to visualize a set of data.Chapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation minimum Q1 Median Q3 maximum (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness
38. 38. Displaying and Exploring DataReviewChapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying and Zero skewness positive skewness negative skewnessexploring data–Dotplot mode=median=mean Mode < Median < Mean Mode > Median > Mean–Stem-leaf–Boxplot–Skewness
39. 39. Displaying and Exploring DataReviewChapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness
40. 40. Displaying and Exploring DataReviewChapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness minimum Q1 Median Q3 maximum
41. 41. ReviewChapter 3:Dispersion–Range–Variance (SD2)–Standard Deviation (SD)–Coefficient of variation (CV)Chapter 4:Displaying andexploring data–Dotplot–Stem-leaf–Boxplot–Skewness •The graph is called a cumulative frequency distribution. •The interquartile range is 45-35=10 years and the median is 40 years a. 10 b.35 c.40 d.45 e.15 f.20 •50% of the employees are between 35 years and 45 years old.
42. 42. What we have learnt?1. Why Failed inStatistics? • Review2. Chapter 1:What is • Chapter 3: DispersionStatistics?A.Why? What? • RangeB.Types of statistics, • Variance (SD2) variablesC.Levels of • Standard Deviation (SD) measurement • Coefficient of variation (CV)3. Chapter 2:Describing Data • Chapter 4: Displaying and exploring dataA.Frequency tables • DotplotB.Frequency • Stem-leaf distributionsC.Graphic • Boxplot presentation • Skewness