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

Graphical Displays of Data

M03- Graphical Displays 1Graphical 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 describefour characteristics of the distribution of a quantitative variable.

M03- Graphical Displays 1Graphical 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).

M03- Graphical Displays 1Graphical Displays 1 4 Department of ISM, University of Alabama, 1995-2003

GraphsGraphs

Histogram

Stem-and-leaf plot

for a singlequantitative

variable

M03- Graphical Displays 1Graphical Displays 1 5 Department of ISM, University of Alabama, 1995-2003

Handout: Data for 100 Households (FAM100)

Income1 Annual income of principal wage earner

Income2 Annual income of secondary wage earner

FamSize Family size

Own? Own or rent (1 = own, 0 = rent)

TotalDebt Total indebtedness (excluding mortgage)

Housing Monthly house payment or rent

Utility Average monthly utility expenditure

City City of residence (1, 2, 3, 4)

Fam100 dataFam100 data

M03- Graphical Displays 1Graphical Displays 1 6 Department of ISM, University of Alabama, 1995-2003

Histogram

10000 20000 30000 40000 50000 60000 70000

5

10

15

20

25

Income1

Frequency

Fam100 dataFam100 data

M03- Graphical Displays 1Graphical 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.

M03- Graphical Displays 1Graphical Displays 1 8 Department of ISM, University of Alabama, 1995-2003

“Distribution” of a Quantitative Variable

Gives an indication of how likelyvalues is different segments of the range of the variable are ofbeing observed.

M03- Graphical Displays 1Graphical 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 6 1 7 2

Fam100 dataFam100 dataStem-and-Leaf Plot

M03- Graphical Displays 1Graphical Displays 1 10 Department of ISM, University of Alabama, 1995-2003

48554 31870 28860 33920 33241 • • •

Income1 Stems Leaves

M03- Graphical Displays 1Graphical Displays 1 11 Department of ISM, University of Alabama, 1995-2003

48554 1531870 1628860 1733920 1833241 •• • 71 • 72 •

Income1 Stems Leaves

Leaf Unit= 100

M03- Graphical Displays 1Graphical Displays 1 12 Department of ISM, University of Alabama, 1995-2003

48554 15031870 15128860 15233920 15333241 •• • 728 • 729 •

Income1 Stems Leaves

Leaf Unit= 10

M03- Graphical Displays 1Graphical Displays 1 13 Department of ISM, University of Alabama, 1995-2003

48554 1 5-9’s31870 2 0-4’s28860 2 5-9’s33920 3 0-4’s33241 3 5-9’s • •• • 7 0-4’s •

Income1 Stems Leaves

Leaf Unit= 1000

SplitStems

M03- Graphical Displays 1Graphical 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 6 7 2

Depth Gauge

M03- Graphical Displays 1Graphical 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.

M03- Graphical Displays 1Graphical Displays 1 16 Department of ISM, University of Alabama, 1995-2003

“Distribution” of a Quantitative Variable

Illustrated by a histogram ora stem-and-leaf plot.

Indicates how likelyvalues is different segments of the range of the variable are ofbeing observed.

M03- Graphical Displays 1Graphical Displays 1 17 Department of ISM, University of Alabama, 1995-2003

Key Features of Data Distributions

M03- Graphical Displays 1Graphical Displays 1 18 Department of ISM, University of Alabama, 1995-2003

Shapes of data distributions

M03- Graphical Displays 1Graphical Displays 1 19 Department of ISM, University of Alabama, 1995-2003

Frequency

_____________ Distribution

M03- Graphical Displays 1Graphical Displays 1 20 Department of ISM, University of Alabama, 1995-2003

Frequency

________________

M03- Graphical Displays 1Graphical Displays 1 21 Department of ISM, University of Alabama, 1995-2003

Frequency

______________

M03- Graphical Displays 1Graphical Displays 1 22 Department of ISM, University of Alabama, 1995-2003

Frequency

_____________

M03- Graphical Displays 1Graphical Displays 1 23 Department of ISM, University of Alabama, 1995-2003

Typical Values:

Center of gravity

"Middle" value

Most frequently occurring value.

M03- Graphical Displays 1Graphical Displays 1 24 Department of ISM, University of Alabama, 1995-2003

Outliers:

Extreme or unusual observations.

Could be mistakes, but not necessarily.

M03- Graphical Displays 1Graphical 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)

M03- Graphical Displays 1Graphical 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)

M03- Graphical Displays 1Graphical 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?

M03- Graphical Displays 1Graphical 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 = _________

M03- Graphical Displays 1Graphical 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 = ________

M03- Graphical Displays 1Graphical 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 ?

Stemplots: “Number of miles put on a sample of rent cars in April”. X = Mileage.

Stem

0

456789

X100

Leaf

4 974

5

4

60

042

6

1

Stemplots: “Number of miles put on a sample of rent cars in April”. X = Mileage.

Stem

0

456789

X100

Leaf

4 974

5

4

60

042

6

1

n =

Max =

Median =

Min =