1. Graphical Displays 1 M03- Graphical Displays 1 1  Department of ISM, University of Alabama, 1995-2003 Graphical Displays of Data

2. Graphical Displays 1 M03- Graphical Displays 1 2  Department of ISM, University of Alabama, 1995-2003 Lesson Objectives  Learn how to construct two graphs for a quantitative variable.  Learn why the “distribution” of a quantitative variable is informative.  Learn how to recognize and describe four characteristics of the distribution of a quantitative variable.

3. Graphical Displays 1 M03- Graphical Displays 1 3  Department of ISM, University of Alabama, 1995-2003 Obtaining Data Files from Outlook Data files from me are in the following location: Public Folders All Public Folders Student Folders Class Related Folders Management Science and Statistics Faculty Dr. Mansfield ST 260 Click the desired posting to select it File –> Save Attachments… There may be more than one version (.txt,.xls).

4. Graphical Displays 1 M03- Graphical Displays 1 4  Department of ISM, University of Alabama, 1995-2003 Graphs  Histogram  Stem-and-leaf plot for a single quantitative variable

5. Graphical Displays 1 M03- Graphical Displays 1 5  Department of ISM, University of Alabama, 1995-2003 Handout: Data for 100 Households (FAM100) Income1Annual income of principal wage earner Income2Annual income of secondary wage earner FamSizeFamily size Own?Own or rent (1 = own, 0 = rent) TotalDebtTotal indebtedness (excluding mortgage) HousingMonthly house payment or rent UtilityAverage monthly utility expenditure CityCity of residence (1, 2, 3, 4) Fam100 data

6. Graphical Displays 1 M03- Graphical Displays 1 6  Department of ISM, University of Alabama, 1995-2003 Histogram 10000200003000040000500006000070000 5 10 15 20 25 Income1 Frequency Fam100 data

7. Graphical Displays 1 M03- Graphical Displays 1 7  Department of ISM, University of Alabama, 1995-2003 Additional Comments  Try using different class intervals; find the histogram that best describes the data distribution.  Always title your graphs and label the axes with meaningful variable names.  Cut-and-paste to paste Excel and Minitab graphs into Word documents for final reports.

8. Graphical Displays 1 M03- Graphical Displays 1 8  Department of ISM, University of Alabama, 1995-2003 “Distribution” of a Quantitative Variable Gives an indication of how likely values is different segments of the range of the variable are of being observed.

9. Graphical Displays 1 M03- Graphical Displays 1 9  Department of ISM, University of Alabama, 1995-2003 Stem-and-leaf plot of Income1 N = 100 Leaf Unit = 1000 2 1 58 6 2 0223 30 2 555566667777778889999999 (22) 3 0001111222222222333344 48 3 5555555666777788889 29 4 00000001111223444 12 4 56667889 4 5 0 3 5 57 1 6 1 7 2 Fam100 data Stem-and-Leaf Plot

10. Graphical Displays 1 M03- Graphical Displays 1 10  Department of ISM, University of Alabama, 1995-2003 48554 31870 28860 33920 33241 Income1 Stems Leaves

11. Graphical Displays 1 M03- Graphical Displays 1 11  Department of ISM, University of Alabama, 1995-2003 48554 15 31870 16 28860 17 33920 18 33241 71 72 Income1 Stems Leaves Leaf Unit = 100

12. Graphical Displays 1 M03- Graphical Displays 1 12  Department of ISM, University of Alabama, 1995-2003 48554 150 31870 151 28860 152 33920 153 33241 728 729 Income1 Stems Leaves Leaf Unit = 10

13. Graphical Displays 1 M03- Graphical Displays 1 13  Department of ISM, University of Alabama, 1995-2003 48554 1 5-9’s 31870 2 0-4’s 28860 2 5-9’s 33920 3 0-4’s 33241 3 5-9’s 7 0-4’s Income1 Stems Leaves Leaf Unit = 1000 Split Stems

14. Graphical Displays 1 M03- Graphical Displays 1 14  Department of ISM, University of Alabama, 1995-2003 1 58 2 0223 2 555566667777778889999999 3 0001111222222222333344 3 5555555666777788889 4 00000001111223444 4 56667889 5 0 5 57 6 7 2 Depth Gauge

15. Graphical Displays 1 M03- Graphical Displays 1 15  Department of ISM, University of Alabama, 1995-2003 Stem-and-Leaf Notes  The “leaf” for a data value is always the first digit to the right of the dividing line.  The “stem” for a data value is all digits to the left of the dividing line.  The “leaf” is always one digit, but a “stem” can be more than one digit.

16. Graphical Displays 1 M03- Graphical Displays 1 16  Department of ISM, University of Alabama, 1995-2003 “Distribution” of a Quantitative Variable  Illustrated by a histogram or a stem-and-leaf plot.  Indicates how likely values is different segments of the range of the variable are of being observed.

17. Graphical Displays 1 M03- Graphical Displays 1 17  Department of ISM, University of Alabama, 1995-2003 Key Features of Data Distributions    

18. Graphical Displays 1 M03- Graphical Displays 1 18  Department of ISM, University of Alabama, 1995-2003 Shapes of data distributions 

19. Graphical Displays 1 M03- Graphical Displays 1 19  Department of ISM, University of Alabama, 1995-2003 Frequency _____________ Distribution

20. Graphical Displays 1 M03- Graphical Displays 1 20  Department of ISM, University of Alabama, 1995-2003 Frequency ________________

21. Graphical Displays 1 M03- Graphical Displays 1 21  Department of ISM, University of Alabama, 1995-2003 Frequency ______________

22. Graphical Displays 1 M03- Graphical Displays 1 22  Department of ISM, University of Alabama, 1995-2003 Frequency _____________

23. Graphical Displays 1 M03- Graphical Displays 1 23  Department of ISM, University of Alabama, 1995-2003 Typical Values:  Center of gravity  "Middle" value  Most frequently occurring value.

24. Graphical Displays 1 M03- Graphical Displays 1 24  Department of ISM, University of Alabama, 1995-2003 Outliers: Extreme or unusual observations. Could be mistakes, but not necessarily.

25. Graphical Displays 1 M03- Graphical Displays 1 25  Department of ISM, University of Alabama, 1995-2003 120 150 180 210 240 270 300 330 14 12 10 8 6 4 2 Frequency Growing Season (Days)

26. Graphical Displays 1 M03- Graphical Displays 1 26  Department of ISM, University of Alabama, 1995-2003 120 150 180 210 240 270 300 330 14 12 10 8 6 4 2 Frequency Growing Season (Days)

27. Graphical Displays 1 M03- Graphical Displays 1 27  Department of ISM, University of Alabama, 1995-2003 120 150 180 210 240 270 300 330 14 12 10 8 6 4 2 Frequency Growing Season (Days) Typical value? Typical value?

28. Graphical Displays 1 M03- Graphical Displays 1 28  Department of ISM, University of Alabama, 1995-2003 120 150 180 210 240 270 300 330 14 12 10 8 6 4 2 Frequency Growing Season (Days) Typical value? Typical value? Mean = _________

29. Graphical Displays 1 M03- Graphical Displays 1 29  Department of ISM, University of Alabama, 1995-2003 120 150 180 210 240 270 300 330 14 12 10 8 6 4 2 Frequency Growing Season (Days) Typical value? Typical value? median = ________

30. Graphical Displays 1 M03- Graphical Displays 1 30  Department of ISM, University of Alabama, 1995-2003 120 150 180 210 240 270 300 330 14 12 10 8 6 4 2 Frequency Growing Season (Days) Outliers ? Outliers ?

31. Stemplots: “Number of miles put on a sample of rent cars in April”. X = Mileage. Stem 04567890456789 X100 Leaf 49 7 4 5 4 6 0 0 42 6 1

32. Stemplots: “Number of miles put on a sample of rent cars in April”. X = Mileage. Stem 04567890456789 X100 Leaf 49 7 4 5 4 6 0 0 42 6 1 n = Max = Median = Min =