1 chapter four understand the use and the importance of graphical presentation; recognise the...

1

Chapter Four

understand the use and the importance of graphical presentation;

recognise the features of varies graphical presentations; and

organise and present the collected data in the most effectively way.

Graphical Presentation

GoalWhen you completed this chapter, you will be able to:

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Graphical Presentation

Problem Area

Collecting the data

Deriving the statistics

Communicating the results

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Graphics can be used as an effective method of visual communication

Graphical Presentation

4

Summary Table

e.g.1 The numbers of reference books in the BA Departmental Library: 40 Statisticbooks, 25 Management books, 80 Accountancy books, 60 Insurance books, and45 other reference books.

Table: Frequency and percentage summary table for BA Departmental Library

Type of books No. of books Percentage of booksStatistic 40 16Management 25 10Accountancy 80 32Insurance 60 24Other 45 18Total 250 100

Note: there are table Title, Description for the table, and Column Heading listed.

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Scatter Diagram

The pattern of the scatter of the points provides insights into the existence and nature of the relationship between the two variables.

Scatter Diagram

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Hours of Study

Exam

. Sco

re

the independent variable X and dependent variable Y

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(a) Direct Linear

0

50

100

0 5 10 15 20

X

Y

(b) Inverse Linear

0

50

100

0 5 10 15 20

X

Y

Scatter Diagram(2)

Possible relationships between two variables:

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(c) Direct Curvilinear

0

50

100

150

200

0 5 10 15 20 25

X

Y

(d) Inverse Curvilinear

0

50

100

150

200

0 5 10 15 20 25

X

Y

Scatter Diagram (3)

Possible relationships between two variables:

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(e) Direct Linear with more scattering

0

20

40

60

80

0 5 10 15 20 25

X

Y

(f) No Relationship

0

10

20

30

40

0 5 10 15 20 25

X

Y

Scatter Diagram (4)

Possible relationships between two variables:

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Line Chart

Line chart use lines between data points to depict the magnitudes of data for two variables or for one variable over time.

The height of the line allows the user to compare magnitude easily.

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(a) Line Chart depicting relationship between two variables

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35 40 45

Income (in '000)

Sa

vin

g (

in '0

00

)

(b) Line Chart depicting Sales over Time

0

10

20

30

40

50

1990 1991 1992 1993 1994

YearS

ale

s (

in m

illio

ns

)

It reflects the moving total, moving average with the seasonal variations taken out - it is the trend line.

Line Chart (2)

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Bar Chart

Bar chart is used to depict the magnitude of data for different qualitative categories or over time.

Several points to note :

1. Bar chart consists of vertical or horizontal bars.

2. all bars should be in same width, but the width of each bar has no special meaning.

3. spaces between bars are suggested to range from one-half the width of a bar to the width of a bar.

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4. scales and guidelines are useful aids in reading a chart and should be included.

5. the axes of the chart should be labelled.

6. any “keys” to interpreting the chart may be included within the body of the chart or below the body of the chart.

7. the title of the chart appears either below or above the body.

8. footnotes and source notes, when appropriate, are given following the title of the chart.

Bar Chart (2)

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Bar Chart for Profit of HKTC Co.

0

200

400

600

800

1000

1200

1989 1990 1991 1992 1993

Year

Pro

fit

(in

'0

00

)

1989

1990

1991

1992

1993

Bar Chart (3)

Note : Bad debts are excludedSource : ABC Co.

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Grouped Bar Chart

Grouped bar chart is used to depict the magnitudes of two or more grouped data items for different qualitative categories or over time.

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Multiple Bars

Multiple Bars: A number of single bar charts superimposed on top of each other.

The purpose of this chart is to contrast more than one sequence of data values.

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Multiple Bars (2)

(a) Bar Chart for percentage of smokers in age group

0

20

40

60

80

100

120

140

Japanese West European East European British

Age Group

Perc

en

tag

e (

%)

Quarter 1

Quarter 2

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(b) Bar chart for quarterly sales of cars

0 20 40 60 80 100 120 140 160

Quarter 1

Quarter 2

Quarter 3

Quarter 4

1993

Sales

British

East European

West European

Japanese

Multiple Bars (3)

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Component Bar Charts

Multiple bars laid directly on top of each other.

Different shading is used to distinguish one set of bars from another.

(c) Component Bar Chart for classification of intaking students

0

100

200

300

400

500

600

700

1990 1991 1992 1993 1994

YearN

o. o

f stu

dent

Mature Student

Form 7

Form 5

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Combination Charts

We may use lines and bars to depict the magnitudes of two or more data values for different categories or for different times.

Combination Chart depicting Actual and Estimated Sales over time

0

10

20

30

40

50

60

1988

1989

1990

1991

1992

1993

1994

1995

1996

Year

Sale

s (in

'000

) Actual Sales

Estimated Sales

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Pie Charts

Pie Chart for proportion of students

Form 5 Students55%Form 7 Students

30%

Mature Students10%

Others5%

Form 5 Students

Form 7 Students

Mature Students

Others

Pie Chart is used effectively to depict the proportion or percentages of a total quantity by colour or shading

Usually five or fewer categories

Shading for the key or makes more interesting

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Exploded Pies

An exploded pie has one or more segments slightly removed.

An exploded pie gives dramatic effect.

Exploded Pie Chart for proportion of students

55%30%

10%5%

Form 5 Students

Form 7 Students

Mature Students

Others

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Three-dimensional Pies

Using three-dimensions in an exploded pie makes the picture much more eye-catching.

3-D Exploded Pie Chart for proportion of students

Form 5 Students55%

Form 7 Students30%

Mature Students10%

Others5%

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Comparative Pies

compare relative proportions at two different times

Comparative Uses of Different Fuels

1955

45%

15%

40%

1985

40%

45%

15%

Coal

Electricity

Gas

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Pictorial Charts

Pictorial Chart for weekly usage of transportation means

0 1 2 3 4 5 6 7 8 9 10

Car

Bus

Bicycle

MTR

Taxi

Tra

nspo

rtat

ion

Mea

ns

Frequency

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Pictorial Charts (2)

Pictorial symbols are used to depict data to gain attention

Difficult to interpret and also misused at times with the 2-d or 3-d symbols.

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General Features of Data

1. Relative sizes of dataThe following statements concern the relative sizes of data,

Women have a greater life expectancy then men. Men generally taller then women. There is less black and white TV sets than colours.

The most effective way to illustrate measurements of relative size is to use Bar Charts.

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General Features of Data (2)

2. Proportional sizes

The most effective way to illustrate proportional sizes of data is to use Pie Charts.

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3. Change in data over time

Between 1961 and 1981, the relative price index of domestic gas fell steadily whereas that of domestic electricity remained the same.

Consumer spending on personal telephones has steadily risen over the past twenty years.

The most effective way to illustrate changes in data over time is to use Line Charts.

General Features of Data (3)

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4.Pictorial Charts can be designed to both convey the necessary message and to catch eye of the casual reader.

5.The use of words is important for summarising a table or picture, e.g. heading and title, and for conclusion.

General Features of Data (4)

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Using ‘chart junk’ No relative basis

In comparing data Batches

Compressing the Vertical axis No zero point on

the Vertical axis

Errors in Presenting Data

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‘ 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 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 Axis

Good Presentation

Quarterly Sales Quarterly Sales

Bad Presentation

0

25

50

Q1 Q2 Q3 Q4

$

0

100

200

Q1 Q2 Q3 Q4

$

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No Zero Point on Vertical Axis

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.

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35

No Zero Point on Vertical Axis

Good Presentation

Monthly Sales Monthly Sales

Bad Presentation

0

20

40

60

J F M A M J

$

36

39

42

45

J F M A M J

$

Graphing the first six months of sales.