STATISTIK DASARSTATISTIK DASAR

ISI:ISI: Tipe dataTipe data Konsep statistik deskriptifKonsep statistik deskriptif Pembuatan grafik statistikPembuatan grafik statistik

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Basic Business Basic Business Statistics Statistics Presenting Data in Presenting Data in

Tables and ChartsTables and Charts

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Chapter TopicsChapter Topics

Organizing numerical dataOrganizing numerical data The ordered array and stem-leaf displayThe ordered array and stem-leaf display

Tabulating and graphing Univariate Tabulating and graphing Univariate numerical datanumerical data Frequency distributions: tables, Frequency distributions: tables,

histograms, polygonshistograms, polygons Cumulative distributions: tables, the OgiveCumulative distributions: tables, the Ogive

Graphing Bivariate numerical dataGraphing Bivariate numerical data

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Chapter TopicsChapter Topics Tabulating and graphing Univariate Tabulating and graphing Univariate

categorical datacategorical data The summary tableThe summary table Bar and pie charts, the Pareto diagramBar and pie charts, the Pareto diagram

Tabulating and graphing Bivariate Tabulating and graphing Bivariate categorical datacategorical data Contingency tablesContingency tables Side by side bar chartsSide by side bar charts

Graphical excellence and common Graphical excellence and common errors in presenting dataerrors in presenting data

(continued)

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Organizing Numerical Organizing Numerical DataData

Numerical Data

Ordered Array

Stem and LeafDisplay

Frequency DistributionsCumulative Distributions

Histograms

Polygons

Ogive

Tables

2 144677

3 028

4 1

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

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

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Data in Data in rawraw form (as collected): form (as collected): 24, 26, 24, 21, 27, 27, 30, 41, 32, 3824, 26, 24, 21, 27, 27, 30, 41, 32, 38

Data inData in ordered arrayordered array from from smallest smallest to largestto largest::

21, 24, 24, 26, 27, 27, 21, 24, 24, 26, 27, 27, 3030, 32, 38, 41, 32, 38, 41 Stem-and-leaf display:Stem-and-leaf display:

Organizing Numerical Organizing Numerical DataData (continued)

2 144677

3 028

4 1

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Tabulating and Graphing Tabulating and Graphing Numerical DataNumerical Data

0

1

2

3

4

5

6

7

10 20 30 40 50 60

Numerical Data

Ordered Array

Stem and LeafDisplay

Histograms Ogive

Tables

2 144677

3 028

4 1

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

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

Frequency DistributionsCumulative Distributions

Polygons

O g ive

0

20

40

60

80

100

120

10 20 30 40 50 60

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Tabulating Numerical Tabulating Numerical Data: Frequency Data: Frequency

DistributionsDistributions Sort raw data in ascending order:Sort raw data in ascending order:

12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 5812, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Find range: Find range: 58 - 12 = 4658 - 12 = 46

Select number of classes: Select number of classes: 55 (usually between 5 and 15)(usually between 5 and 15)

Compute class interval (width): Compute class interval (width): 10 10 (46/5 then round up)(46/5 then round up)

Determine class boundaries (limits): Determine class boundaries (limits): 10, 20, 30, 40, 10, 20, 30, 40,

50, 6050, 60

Compute class midpoints: Compute class midpoints: 15, 25, 35, 45, 5515, 25, 35, 45, 55

Count observations & assign to classesCount observations & assign to classes

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Frequency Distributions, Relative Frequency Distributions, Relative Frequency Distributions and Frequency Distributions and

Percentage DistributionsPercentage Distributions

Class Frequency

10 but under 20 3 .15 15

20 but under 30 6 .30 30

30 but under 40 5 .25 25

40 but under 50 4 .20 20

50 but under 60 2 .10 10

Total 20 1 100

RelativeFrequency

Percentage

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

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Graphing Numerical Graphing Numerical Data: Data:

The HistogramThe Histogram

Histogram

0

3

65

4

2

001234567

5 15 25 36 45 55 More

Fre

qu

en

cy

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

No Gaps Between

Bars

Class MidpointsClass Boundaries

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Graphing Numerical Graphing Numerical Data: Data:

The Frequency PolygonThe Frequency Polygon

Frequency

0

1

2

3

4

5

6

7

5 15 25 36 45 55 More

Class Midpoints

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

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Tabulating Numerical Tabulating Numerical Data: Data:

Cumulative FrequencyCumulative Frequency

Cumulative CumulativeClass Frequency % Frequency

10 but under 20 3 15

20 but under 30 9 45

30 but under 40 14 70

40 but under 50 18 90

50 but under 60 20 100

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

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Graphing Numerical Graphing Numerical Data: Data:

The Ogive (Cumulative % The Ogive (Cumulative % Polygon)Polygon)

Ogive

0

20

40

60

80

100

10 20 30 40 50 60

Class Boundaries (Not Midpoints)

Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

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Graphing Bivariate Graphing Bivariate Numerical Data (Scatter Numerical Data (Scatter

Plot)Plot)Mutual Funds Scatter Plot

0

10

20

30

40

0 10 20 30 40

Net Asset Values

Tota

l Yea

r to

D

ate

Ret

urn

(%)

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Tabulating and Graphing Tabulating and Graphing Categorical Categorical

Data:Univariate DataData:Univariate DataCategorical Data

Tabulating Data

The Summary Table

Graphing Data

Pie Charts

Pareto DiagramBar Charts

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Summary TableSummary Table(for an Investor’s Portfolio)(for an Investor’s Portfolio)

Investment Category Amount Percentage (in thousands $)

Stocks 46.5 42.27

Bonds 32 29.09

CD 15.5 14.09

Savings 16 14.55

Total 110 100

Variables are Categorical

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Graphing Categorical Graphing Categorical Data: Univariate DataData: Univariate Data

Categorical Data

Tabulating Data

The Summary Table

0 1 0 2 0 3 0 4 0 5 0

S to c k s

B o n d s

S a vin g s

C D

Graphing Data

Pie Charts

Pareto DiagramBar Charts

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

S to c k s B o n d s S a vin g s C D

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

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Bar ChartBar Chart(for an Investor’s Portfolio)(for an Investor’s Portfolio)

Investor's Portfolio

0 10 20 30 40 50

Stocks

Bonds

CD

Savings

Amount in K$

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Pie ChartPie Chart (for an Investor’s Portfolio)(for an Investor’s Portfolio)

Percentages are rounded to the nearest percent.

Amount Invested in K$

Savings

15%

CD 14%

Bonds

29%

Stocks

42%

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Pareto DiagramPareto Diagram

Axis for line graph shows

cumulative % invested

Axis for bar

chart shows

% invested in each

category

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Stocks Bonds Savings CD

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

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Tabulating and Graphing Tabulating and Graphing Bivariate Categorical Bivariate Categorical

DataData Contingency tables: Contingency tables: investment in thousands investment in thousands

of dollarsof dollarsInvestment Investor A Investor B Investor C Total Category

Stocks 46.5 55 27.5 129

Bonds 32 44 19 95

CD 15.5 20 13.5 49

Savings 16 28 7 51

Total 110 147 67 324

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Tabulating and Graphing Tabulating and Graphing Bivariate Categorical Bivariate Categorical

DataData Side by side chartsSide by side charts

Comparing Investors

0 10 20 30 40 50 60

S toc k s

B onds

CD

S avings

Inves tor A Inves tor B Inves tor C

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Principles of Graphical Principles of Graphical ExcellenceExcellence

Presents data in a way that provides Presents data in a way that provides substance, statistics and designsubstance, statistics and design

Communicates complex ideas with Communicates complex ideas with clarity, precision and efficiencyclarity, precision and efficiency

Gives the largest number of ideas in Gives the largest number of ideas in the most efficient mannerthe most efficient manner

Almost always involves several Almost always involves several dimensionsdimensions

Tells the truth about the dataTells the truth about the data

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Using “chart junk”Using “chart junk” Failing to provide a relative Failing to provide a relative

basis in comparing data basis in comparing data between groups between groups

Compressing the vertical axisCompressing the vertical axis Providing no zero point on the Providing no zero point on the

vertical axisvertical axis

Errors in Presenting Errors in Presenting DataData

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““Chart Junk”Chart Junk”

Good Presentation

1960: $1.00

1970: $1.60

1980: $3.10

1990: $3.80

Minimum Wage Minimum Wage

0

2

4

1960 1970 1980 1990

$

Bad Presentation

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No Relative BasisNo Relative Basis

Good PresentationA’s received by

students.A’s received by

students.

Bad Presentation

0

200

300

FR SO JR SR

Freq.

10

30

FR SO JR SR

%

FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior

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Compressing Vertical Compressing Vertical AxisAxis

Good Presentation

Quarterly Sales Quarterly Sales

Bad Presentation

0

25

50

Q1 Q2 Q3 Q4

$

0

100

200

Q1 Q2 Q3 Q4

$

28

No Zero Point on Vertical No Zero Point on Vertical AxisAxis

Good Presentation

Monthly SalesMonthly Sales

Bad Presentation

0

39

42

45

J F M A M J

$

36

39

42

45

J F M A M J

$

Graphing the first six months of sales.

36

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Chapter SummaryChapter Summary

Organized numerical dataOrganized numerical data The ordered array and stem-leaf displayThe ordered array and stem-leaf display

Tabulated and graphed univariate Tabulated and graphed univariate numerical datanumerical data Frequency distributions: tables, histograms, Frequency distributions: tables, histograms,

polygonpolygon Cumulative distributions: tables and the Cumulative distributions: tables and the

OgiveOgive

Graphed bivariate numerical dataGraphed bivariate numerical data

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Chapter SummaryChapter Summary Tabulated and graphed univariate Tabulated and graphed univariate

categorical datacategorical data The summary tableThe summary table Bar and pie charts, the Pareto diagramBar and pie charts, the Pareto diagram

Tabulated and graphed bivariate Tabulated and graphed bivariate categorical datacategorical data Contingency tablesContingency tables Side by side chartsSide by side charts

Discussed graphical excellence and Discussed graphical excellence and common errors in presenting datacommon errors in presenting data

(continued)