basic statistic chap02

Chapter 2

Presenting Data in Tables and ChartsStatistics for ManagersUsing Microsoft Excel 4th Edition

Statistics for Managers Using Microsoft Excel, 4e 2004 Prentice-Hall, Inc.Chap 2-*

Chapter GoalsAfter completing this chapter, you should be able to: Create an ordered array and a stem-and-leaf displayConstruct and interpret a frequency distribution, histogram, polygon, and ogive Create and interpret bar charts, pie charts, and scatter diagrams for numerical dataPresent and interpret categorical data in bar charts and pie chartsDescribe appropriate and inappropriate ways to display data graphically


Organizing and Presenting Data GraphicallyData in raw form are usually not easy to use for decision makingSome type of organization is neededTableGraphTechniques reviewed here:Ordered ArrayStem-and-Leaf DisplayFrequency Distributions and HistogramsBar charts and pie chartsContingency tables


Tables and Charts for Numerical DataNumerical DataOrdered ArrayStem and LeafDisplayHistogramPolygonOgiveFrequency Distributions andCumulative Distributions


The Ordered ArrayJust a sorted list of data: Shows range (min to max) Provides some signals about variability within the range May help identify outliers (unusual observations) If the data set is large, the ordered array is less useful


The Ordered ArrayData in raw form (as collected):

24, 26, 24, 21, 27, 27, 30, 41, 32, 38

Data in ordered array from smallest to largest: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41(continued)


Stem and Leaf DiagramA simple way to see distribution details in a data set

Separate the sorted data series into leading digits (the stem) and the trailing digits (the leaves)


ExampleHere, use the 10s digit for the stem unit:Data in ordered array:21, 24, 24, 26, 27, 27, 30, 32, 38, 4121 is shown as38 is shown asStem Leaf 2 1 3 8


ExampleCompleted Stem-and-leaf diagram:(continued)Data in ordered array:21, 24, 24, 26, 27, 27, 30, 32, 38, 41

StemLeaves21 4 4 6 7 730 2 841


Using other stem unitsUsing the 100s digit as the stem:Round off the 10s digit to form the leaves

613 would become 6 1776 would become 7 8 . . .1224 becomes 12 2

Stem Leaf


Using other stem unitsUsing the 100s digit as the stem:The completed stem-and-leaf display:

Stem Leaves(continued) 6 1 3 6 7 2 2 5 8 8 3 4 6 6 9 9 9 1 3 3 6 8 10 3 5 6 11 4 7 12 2Data:

613, 632, 658, 717,722, 750, 776, 827,841, 859, 863, 891,894, 906, 928, 933,955, 982, 1034, 1047,1056, 1140, 1169, 1224


Tabulating Numerical Data: Frequency DistributionsA frequency distribution is a list or a table containing class groupings (categories or ranges within which the data falls) ...and the corresponding frequencies with which data falls within each grouping or category


Why Use Frequency Distributions?A frequency distribution is a way to summarize dataThe distribution condenses the raw data into a more useful form... and allows for a quick visual interpretation of the dataand easy graphical display


Class Intervals and Class BoundariesIf each class grouping has the same widthDetermine the width of each interval byUse at least 5 but no more than 15 groupingsClass boundaries never overlapRound up the interval width to get desirable endpoints


Approximate Number of ClassesExcel uses the square root of n.

ObservationsClassesLess than 503-650-2006-9200-10008-12More than 100010-15


Frequency Distribution ExampleA manufacturer of insulation randomly selects 20 winter days and records the daily high temperature 24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27


Frequency Distribution ExampleSort raw data in ascending order: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58Find range: 58 - 12 = 46Select number of classes: 5 (usually between 5 and 15)Compute class interval (width): 10 (46/5 then round up)Determine class boundaries (limits): 10, 20, 30, 40, 50, 60Compute class midpoints: 15, 25, 35, 45, 55Count observations & assign to classes(continued)


Frequency Distribution Example

Class Frequency10 but less than 20 3 .15 1520 but less than 30 6 .30 3030 but less than 40 5 .25 25 40 but less than 50 4 .20 2050 but less than 60 2 .10 10 Total 20 1.00 100RelativeFrequency PercentageData in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58(continued)


Graphing Numerical Data: The HistogramA graph of the data in a frequency distribution is called a histogram The class boundaries (or class midpoints) are shown on the horizontal axisfrequency is measured on the vertical axisBars of the appropriate heights can be used to represent the number of observations within each class


Histogram ExampleClass Midpoints(No gaps between bars)Class10 but less than 20 15 320 but less than 30 25 630 but less than 40 35 540 but less than 50 45 450 but less than 60 55 2FrequencyClass Midpoint

Chart2

0

3

6

5

4

2

0

Frequency

Frequency

Histogram: Daily High Temperature

Sheet4

BinFrequency

105

200

300

400

500

More0

Sheet5

BinFrequency

100

203

307

404

504

602

More0

Sheet5

0

0

0

0

0

0

0

Frequency

Bin

Frequency

Histogram

Sheet6

BinFrequencyCumulative %BinFrequencyCumulative %

50.00%35630.00%

15210.00%45555.00%

25430.00%25475.00%

35660.00%15285.00%

45585.00%55295.00%

55295.00%651100.00%

651100.00%50100.00%

More0100.00%More0100.00%

Sheet6

00

00

00

00

00

00

00

00

Frequency

Cumulative %

Bin

Frequency

Histogram

Sheet7

BinFrequency

50

153

256

355

454

552

More0

Sheet7

0

0

0

0

0

0

0

Frequency

Frequency

Histogram

Sheet8

BinFrequency

00

102

204

306

405

502

601

More0

Sheet8

0

0

0

0

0

0

0

0

Frequency

Frequency

Histogram

Sheet9

BinFrequency

00

103

207

304

404

502

More0

Sheet9

0

0

0

0

0

0

0

Frequency

Bin

Frequency

Histogram

Sheet10

Sheet11

BinFrequency

9.93

19.96

20.91

30.94

40.94

50.92

More0

Sheet11

0

0

0

0

0

0

0

Frequency

Bin

Frequency

Histogram

Sheet12

BinFrequency

9.93

19.96

29.95

39.94

49.92

59.90

More0

Sheet12

0

0

0

0

0

0

0

Frequency

Frequency

Histogram

Sheet2

29.9

319.9

729.9

1139.9

1249.9

1459.9

16

17

17

20

21

25

27

28

31

33

34

36

43

48

Sheet3

103

206

305

404

502


Histograms in ExcelSelectTools/Data Analysis1


Choose Histogram23Input data range and bin range (bin range is a cell range containing the upper class boundaries for each class grouping)

Select Chart Output and click OKHistograms in Excel(continued)(


Questions for Grouping Data into Classes1.How wide should each interval be? (How many classes should be used?)

2.How should the endpoints of the intervals be determined?Often answered by trial and error, subject to user judgmentThe goal is to create a distribution that is neither too "jagged" nor too "blocky Goal is to appropriately show the pattern of variation in the data


How Many Class Intervals?Many (Narrow class intervals)may yield a very jagged distribution with gaps from empty classes Can give a poor indication of how frequency varies across classes

Few (Wide class intervals)may compress variation too much and yield a blocky distributioncan obscure important patterns of variation.(X axis labels are upper class endpoints)

Chart2

0

10

10

0

Frequency

Temperature

Frequency

Sheet4

BinFrequency

00

3010

6010

More0

Sheet4

Frequency

Temperature

Frequency

Sheet5

BinFrequency

00

203

4011

606

More0

Sheet5

Frequency

Temperature

Frequency

Sheet1

12

13Bins

171020

2120420

2430640

2440860

265010

276012

2714

3016

3218

3520

3722

3824

4126

4328

4430

4632

5334

5836

38

40

42

44

46

48

50

52

54

56

58

60

62

Sheet2

Sheet3

Chart3

0

0

1

1

1

3

3

2

1

2

3

1

0

1

1

0

Frequency

Temperature

Frequency

Sheet4

BinFrequency

00

3010

6010

More0

Sheet4

Frequency

Temperature

Frequency

Sheet5

BinFrequency

00

203

4011

606

More0

Sheet5

Frequency

Temperature

Frequency

Sheet6

BinFrequency

20

40

60

80

100

121

141

160

181

200

221

242

261

282

301

321

340

361

382

400

421

442

461

480

500

520

541

560

581

600

620

More0

Sheet6

Frequency

Temperature

Frequency

Sheet7

BinFrequency

40

80

121

161

201

243

283

322

361

402

443

481

520

561

601

More0

Sheet7

Frequency

Temperature

Frequency

Sheet1

12

13Bins

1710204

21204208

243064012

244086016

26501020

27601224

271428

301632

321836

352040

372244

382448

412652

432856

443060

4632

5334

5836

38

40

42

44

46

48

50

52

54

56

58

60

62

Sheet2

Sheet3


Graphing Numerical Data: The Frequency PolygonClass MidpointsClass 1 but less than 10 5 0 10 but less than 20 15 320 but less than 30 25 630 but less than 40 35 540 but less than 50 45 450 but less than 60 55 2More than 60 65 0FrequencyClass Midpoint(In a percentage polygon the vertical axis would be defined to show the percentage of observations per class)

Chart3

0

3

6

5

4

2

0

Frequency

Frequency

Frequency Polygon: Daily High Temperature

Sheet4

BinFrequency

105

200

300

400

500

More0

Sheet5

BinFrequency

100

203

307

404

504

602

More0

Sheet5

0

0

0

0

0

0

0

Frequency

Bin

Frequency

Histogram

Sheet6


50.00%35630.00%

15210.00%45555.00%

25430.00%25475.00%

35660.00%15285.00%

45585.00%55295.00%

55295.00%651100.00%

651100.00%50100.00%

More0100.00%More0100.00%

Sheet6

00

00

00

00

00

00

00

00

Frequency

Cumulative %

Bin

Frequency

Histogram

Sheet7

BinFrequency

50

153

256

355

454

552

More0

Sheet7

0

0

0

0

0

0

0

Frequency

Frequency

Histogram

Sheet8

0

0

0

0

0

0

0

Frequency

Sheet9

BinFrequency

00

102

204

306

405

502

601

More0

Sheet9

0

0

0

0

0

0

0

0

Frequency

Frequency

Histogram

Sheet10

BinFrequency

00

103

207

304

404

502

More0

Sheet10

0

0

0

0

0

0

0

Frequency

Bin

Frequency

Histogram

Sheet11

Sheet12

BinFrequency

9.93

19.96

20.91

30.94

40.94

50.92

More0

Sheet12

0

0

0

0

0

0

0

Frequency

Bin

Frequency

Histogram

Sheet2

BinFrequency

9.93

19.96

29.95

39.94

49.92

59.90

More0

Sheet2

0

0

0

0

0

0

0

Frequency

Frequency

Histogram

Sheet3

29.9

319.9

729.9

1139.9

1249.9

1459.9

16

17

17

20

21

25

27

28

31

33

34

36

43

48

103

206

305

404

502


Tabulating Numerical Data: Cumulative FrequencyClass10 but less than 20 3 15 less than 20 3 1520 but less than 30 6 30 less than 30 9 4530 but less than 40 5 25 less than 40 14 7040 but less than 50 4 20 less than 50 18 9050 but less than 60 2 10 less than 60 20 100 Total 20 100 %Cumulative PercentageData in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58Freq.Cumulative FrequencyClass


Graphing Cumulative Frequencies: The Ogive (Cumulative % Polygon)Class Boundaries (Not Midpoints)Class less than 10 10 0 less than 20 20 15 less than 30 30 45 less than 40 40 70 less than 50 50 90 less than 60 60 100Cumulative PercentageLower class boundary

Chart1

0

15

45

70

90

100

Frequency

Cumulative Percentage

Ogive: Daily High Temperature

Sheet4

BinFrequency

105

200

300

400

500

More0

Sheet5

BinFrequency

100

203

307

404

504

602

More0

Sheet5

0

3

7

4

4

2

0

Frequency

Bin

Frequency

Histogram

Sheet6


50.00%35630.00%

15210.00%45555.00%

25430.00%25475.00%

35660.00%15285.00%

45585.00%55295.00%

55295.00%651100.00%

651100.00%50100.00%

More0100.00%More0100.00%

Sheet6

60.3

50.55

40.75

20.85

20.95

11

01

01

Frequency

Cumulative %

Bin

Frequency

Histogram

Sheet7

BinFrequency

100

2015

3045

4070

5090

60100

Sheet7

0

0

0

0

0

0

0

Frequency

Sheet8

0

0

0

0

0

0

0

Frequency

Ogive

Sheet9

BinFrequency

00

102

204

306

405

502

601

More0

Sheet9

0

2

4

6

5

2

1

0

Frequency

Frequency

Histogram

Sheet10

BinFrequency

00

103

207

304

404

502

More0

Sheet10

0

3

7

4

4

2

0

Frequency

Bin

Frequency

Histogram

Sheet11

Sheet12

BinFrequency

9.93

19.96

20.91

30.94

40.94

50.92

More0

Sheet12

3

6

1

4

4

2

0

Frequency

Bin

Frequency

Histogram

Sheet2

BinFrequency

9.93

19.96

29.95

39.94

49.92

59.90

More0

Sheet2

3

6

5

4

2

0

0

Frequency

Frequency

Histogram

Sheet3

29.9

319.9

729.9

1139.9

1249.9

1459.9

16

17

17

20

21

25

27

28

31

33

34

36

43

48

103

206

305

404

502


Scatter Diagrams are used for bivariate numerical data Bivariate data consists of paired observations taken from two numerical variables

The Scatter Diagram:one variable is measured on the vertical axis and the other variable is measured on the horizontal axisScatter Diagrams


Scatter Diagram Example

Volume per dayCost per day231252614029146331603816742170501885519560200

Chart2

125

140

146

160

167

170

188

195

200

Cost per day

Volume per Day

Cost per Day

Cost per Day vs. Production Volume

Sheet1

Volume per dayCost per day

23125

26140

29146

33160

38167

42170

50188

55195

60200

Sheet1

0

0

0

0

0

0

0

0

0

Cost per day

Volume per Day

Cost per Day

Production Volume vs. Cost per Day

Sheet2

Sheet3


Scatter Diagrams in ExcelSelect the chart wizard12Select XY(Scatter) option, then click NextWhen prompted, enter the data range, desired legend, and desired destination to complete the scatter diagram3


Tables and Charts for Categorical Data: Univariate DataCategorical DataGraphing DataPie ChartsPareto DiagramBar ChartsTabulating Data Summary Table


The Summary TableExample: Current Investment Portfolio

Investment Amount Percentage Type (in thousands $) (%)

Stocks 46.5 42.27

Bonds 32.0 29.09

CD 15.5 14.09

Savings 16.0 14.55

Total 110.0 100.0(Variables are Categorical)Summarize data by category


Bar and Pie ChartsBar charts and Pie charts are often used for qualitative (category) data

Height of bar or size of pie slice shows the frequency or percentage for each category


Bar Chart ExampleInvestment Amount PercentageType (in thousands $) (%)

Stocks 46.5 42.27

Bonds 32.0 29.09

CD 15.5 14.09

Savings 16.0 14.55

Total 110.0 100.0Current Investment Portfolio

Chart4

46.5

32

15.5

16

Amount in K$

Amount in $1000's

Investor's Portfolio

Sheet4

BinFrequency

105

200

300

400

500

More0

Sheet5

BinFrequency

100

203

307

404

504

602

More0

Sheet5

0

3

7

4

4

2

0

Frequency

Bin

Frequency

Histogram

Sheet6


50.00%35630.00%

15210.00%45555.00%

25430.00%25475.00%

35660.00%15285.00%

45585.00%55295.00%

55295.00%651100.00%

651100.00%50100.00%

More0100.00%More0100.00%

Sheet6

60.3

50.55

40.75

20.85

20.95

11

01

01

Frequency

Cumulative %

Bin

Frequency

Histogram

Sheet1

Investment typesAmount in K$%

Stocks46.5

Bonds32

CD15.5

Savings16

Sheet1

0

0

0

0

Amount in K$

Amount in K$

Investor's Porfolio

Sheet7

BinFrequency

50

153

259

3514

4518

5520

Sheet7

0

0

0

0

0

0

0

Frequency

Sheet8

0

0

0

0

0

0

0

Frequency

Ogive

Sheet9

BinFrequency

00

102

204

306

405

502

601

More0

Sheet9

0

2

4

6

5

2

1

0

Frequency

Frequency

Histogram

Sheet10

BinFrequency

00

103

207

304

404

502

More0

Sheet10

0

3

7

4

4

2

0

Frequency

Bin

Frequency

Histogram

Sheet11

Sheet12

BinFrequency

9.93

19.96

20.91

30.94

40.94

50.92

More0

Sheet12

3

6

1

4

4

2

0

Frequency

Bin

Frequency

Histogram

Sheet2

BinFrequency

9.93

19.96

29.95

39.94

49.92

59.90

More0

Sheet2

3

6

5

4

2

0

0

Frequency

Frequency

Histogram

Sheet3

29.9

319.9

729.9

1139.9

1249.9

1459.9

16

17

17

20

21

25

27

28

31

33

34

36

43

48

103

206

305

404

502


Pie Chart ExamplePercentages are rounded to the nearest percentCurrent Investment Portfolio Savings 15%CD 14%Bonds 29%Stocks42%Investment Amount PercentageType (in thousands $) (%)

Stocks 46.5 42.27

Bonds 32.0 29.09

CD 15.5 14.09

Savings 16.0 14.55

Total 110.0 100.0

Chart1

42.2727272727

29.0909090909

14.0909090909

14.5454545455

Sheet4

BinFrequency

105

200

300

400

500

More0

Sheet5

BinFrequency

100

203

307

404

504

602

More0

Sheet5

0

0

0

0

0

0

0

Frequency

Bin

Frequency

Histogram

Sheet6


50.00%35630.00%

15210.00%45555.00%

25430.00%25475.00%

35660.00%15285.00%

45585.00%55295.00%

55295.00%651100.00%

651100.00%50100.00%

More0100.00%More0100.00%

Sheet6

00

00

00

00

00

00

00

00

Frequency

Cumulative %

Bin

Frequency

Histogram

Sheet13

InvestmentInvestor AInvestor BInvestor C

Stocks46.55527.542.2727272727

Bonds32441929.0909090909

CD15.52013.514.0909090909

Savings1628714.5454545455

Sheet13

000

000

000

000

Investor A

Investor B

Investor C

Comparing Investors

Sheet1

0

0

0

0

Sheet7

Investment typesPercentageCumulative

Stocks42.2742.27

Bonds29.0971.36

Savings14.5585.91

CD14.09100

Sheet7

0

0

0

0

Percentage

Sheet8

0

0

0

0

Percentage

Sheet9

00

00

00

00

&A

Page &P

Percentage

Cumulative

Sheet10

BinFrequency

50

153

259

3514

4518

5520

Sheet10

0

0

0

0

0

0

0

Frequency

Sheet11

0

0

0

0

0

0

0

Frequency

Ogive

Sheet12

BinFrequency

00

102

204

306

405

502

601

More0

Sheet12

0

0

0

0

0

0

0

0

Frequency

Frequency

Histogram

Sheet2

BinFrequency

00

103

207

304

404

502

More0

Sheet2

0

0

0

0

0

0

0

Frequency

Bin

Frequency

Histogram

Sheet3

BinFrequency

9.93

19.96

20.91

30.94

40.94

50.92

More0

0

0

0

0

0

0

0

Frequency

Bin

Frequency

Histogram

BinFrequency

9.93

19.96

29.95

39.94

49.92

59.90

More0

0

0

0

0

0

0

0

Frequency

Frequency

Histogram

29.9

319.9

729.9

1139.9

1249.9

1459.9

16

17

17

20

21

25

27

28

31

33

34

36

43

48

103

206

305

404

502


Pareto Diagram Examplecumulative % invested (line graph)% invested in each category (bar graph)Current Investment Portfolio

Pareto

0.420.42

0.290.71

0.150.86

0.141


Tabulating and Graphing Multivariate Categorical DataContingency Table for Investment Choices ($1000s)Investment Investor A Investor B Investor C Total Category

Stocks 46.5 55 27.5 129Bonds 32.0 44 19.0 95

CD 15.5 20 13.5 49Savings 16.0 28 7.0 51

Total 110.0 147 67.0 324 (Individual values could also be expressed as percentages of the overall total, percentages of the row totals, or percentages of the column totals)


Tabulating and Graphing Multivariate Categorical DataSide by side bar charts(continued)

Chart16

Stocks46.55527.5

Bonds324419

CD15.52013.5

Savings16287

Investor A

Investor B

Investor C

Comparing Investors

Sheet4

BinFrequency

105

200

300

400

500

More0

Sheet5

BinFrequency

100

203

307

404

504

602

More0

Sheet5

0

3

7

4

4

2

0

Frequency

Bin

Frequency

Histogram

Sheet6


50.00%35630.00%

15210.00%45555.00%

25430.00%25475.00%

35660.00%15285.00%

45585.00%55295.00%

55295.00%651100.00%

651100.00%50100.00%

More0100.00%More0100.00%

Sheet6

60.3

50.55

40.75

20.85

20.95

11

01

01

Frequency

Cumulative %

Bin

Frequency

Histogram

Sheet13

InvestmentInvestor AInvestor BInvestor C

Stocks46.55527.5

Bonds324419

CD15.52013.5

Savings16287

Sheet13

Investor A

Investor B

Investor C

Comparing Investors

Sheet1

Investment typesPercentageCumulative

Stocks42.2742.27

Bonds29.0971.36

Savings14.5585.91

CD14.09100

Sheet1

Percentage

Sheet7

Percentage

Sheet8

&A

Page &P

Percentage

Cumulative

Sheet9

BinFrequency

50

153

259

3514

4518

5520

Sheet9

Frequency

Sheet10

Frequency

Ogive

Sheet11

BinFrequency

00

102

204

306

405

502

601

More0

Sheet11

0

2

4

6

5

2

1

0

Frequency

Frequency

Histogram

Sheet12

BinFrequency

00

103

207

304

404

502

More0

Sheet12

0

3

7

4

4

2

0

Frequency

Bin

Frequency

Histogram

Sheet2

Sheet3

BinFrequency

9.93

19.96

20.91

30.94

40.94

50.92

More0

Sheet3

3

6

1

4

4

2

0

Frequency

Bin

Frequency

Histogram

BinFrequency

9.93

19.96

29.95

39.94

49.92

59.90

More0

3

6

5

4

2

0

0

Frequency

Frequency

Histogram

29.9

319.9

729.9

1139.9

1249.9

1459.9

16

17

17

20

21

25

27

28

31

33

34

36

43

48

103

206

305

404

502


Side-by-Side Chart ExampleSales by quarter for three sales territories:


Principles of Graphical ExcellencePresent data in a way that provides substance, statistics and designCommunicate complex ideas with clarity, precision and efficiencyGive the largest number of ideas in the most efficient mannerExcellence almost always involves several dimensionsTells the truth about the data


Chart Junk and Lie FactorGood Presentation1960: $1.00 1970: $1.60 1980: $3.101990: $3.80Minimum WageMinimum Wage0241960197019801990$Bad Presentation


No Relative BasisGood PresentationAs received by students.As received by students.Bad Presentation0200300FRSOJRSRFreq.10%30%FRSOJRSRFR = Freshmen, SO = Sophomore, JR = Junior, SR = Seniorlisten10020% 0% %


Compressing Vertical AxisGood PresentationQuarterly SalesQuarterly SalesBad Presentation02550Q1Q2Q3Q4$0100200Q1Q2Q3Q4$


No Zero Point On Vertical AxisMonthly Sales 0394245JFMAMJ$360204060JFMAMJ$Good PresentationsMonthly SalesBad Presentation36394245JFMAMJ$Graphing the first six months of salesor


Chapter SummaryData in raw form are usually not easy to use for decision making -- Some type of organization is needed: Table GraphTechniques reviewed in this chapter:Ordered array and stem-and-leaf displayFrequency distributions and histogramsPolygons and ogivesScatter diagrams for bivariate dataBar charts, pie charts, and Pareto diagramsContingency tables and side-by-side bar charts

basic statistic chap02

Documents

Transcript of basic statistic chap02