QBM117Business Statistics

Descriptive Statistics

Graphical Presentation of Qualitative Data

Objective

• To summarise qualitative data using pie charts and bar charts

Graphical Methods for Qualitative Data

• Qualitative data are categorical observations.

• Qualitative data is often given in the form of a table with one column containing the categories and another column containing the number of observations (frequencies) in each category.

• Qualitative data is best presented as either a pie chart or a bar chart.

Example 2.3 from text

The student placement office at a university in New South Wales conducted a survey of last year’s graduates from the Faculty of Economics and Commerce to determine the general areas in which the graduates found jobs. Each graduate was asked in which area he or she found a job. The results are given in the following table.

Area of Employment Number of Graduates

Accounting 73

Finance 52

General Management 36

Marketing 64

Other 28

Total 253

Pie Charts

• The most popular graphical method for qualitative data is the pie chart.

• A pie chart represents data in the form of sections of a circle.

• Each section represents a category.

• The size of the section is proportional to the number of observations in the category.

Constructing a Pie Chart

• First we need to calculate the proportion of observations in each category.

• We draw a circle and divide it in to sections.

• The angle of each section of the circle is equal to the category’s proportion multiplied by 360°.

• Pie charts can be constructed easily using Excel.

Example 2.3 revisited

Construct a pie chart of the data.

Area of Employment Number of Graduates

Accounting 73

Finance 52

General Management 36

Marketing 64

Other 28

Total 253

Employment

Area

Number of

Graduates

Proportion of

Graduates

Angle of

Circle

Accounting 73 73/253=0.2885

0.2885x360°=104°

Finance 52 52/253=0.2055

0.2055x360°=74°

Management

36 36/253=0.1423

0.1423x360°=51°

Marketing 64 64/253=0.2530

0.2530x360°=91°

Other 28 28/253=0.1107

0.1107x360°=40°

Total 253 1.0000 360°

Pie Chart of Area of Employment

Accounting29%

Finance21%General

Management14%

Marketing25%

Other11%

Bar Chart

• An alternative graphical method for qualitative data is the bar chart.

• In a bar chart, each category is depicted by a bar.

• The length of each bar represents the number of observations falling into the category.

Constructing a Bar Chart

• The categories are placed on the horizontal axis.

• Frequency is placed on the vertical axis.

• A bar is drawn for each category from the horizontal axis to a height that corresponds to the frequency of the category.

• The bars are of equal width.

• Each bar is separated from the others to enhance the visual presentation.

Example 2.3 revisited

Construct a bar chart of the data.

Area of Employment Number of Graduates

Accounting 73

Finance 52

General Management 36

Marketing 64

Other 28

Total 253

Bar Chart of Employment Areas

0

10

20

30

40

50

60

70

80

Accounting Finance GeneralManagement

Marketing Other

Areas of Employment

Nu

mb

er o

f G

rad

uat

es

Pie Chart or Bar Chart?

• The selection of chart is dependent on the intention of the user.

• If we want to emphasize the proportion of observations in each category then it is best to use a pie chart.

• If we want to compare categories it is best to use a bar chart.

Pie Charts and Bar Charts in Excel

• We are going to produce a bar chart of the rank data and a pie chart of the faculty data from Exercise 2.46 from the text.

• We are given the raw data and need to construct a pivot table to summarise the data before we can construct the charts.

Bar Chart of Rank of University Academics

0

20

40

60

80

100

120

140

160

180

associate professor lecturer professor senior lecturer

Rank

Nu

mb

er o

f A

cad

emic

s

Pie Chart of Faculty of University Academics

associate professor41%

lecturer13%

professor14%

senior lecturer32%

Multiple Qualitative Variables

• Often we are interested in more than one set of qualitative data.

• For example, we may have qualitative data for a number of years.

• We could do a separate pie chart for each year.

• Or we could display all the information on a single bar chart.

Bar charts for Multiple Sets of Data

• There are two types of bar charts that we use to display multiple sets of qualitative data.

- grouped bar chart

- component bar chart

• The selection of chart depends on the type of data and what you want to emphasize.

Grouped Bar chart

Consider the data in Table 2.12 on page 42 of the text (pg 40 abridged).

The data are the new passenger vehicle registrations in Australia by leading car manufacturers for 1997 and 1998.

We will construct a grouped bar chart of this data in Excel.

Grouped Bar Chart of the New Passenger Vehicle Registrations in Australia by Leading Car

Manufacturers for 1997 and 1998

0

2000

4000

6000

8000

10000

12000

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Ho

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Nis

san

Su

ba

ru

To

yota

Oth

ers

Manufacturer

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egis

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Oct-97

Oct-98

Component Bar Chart

Consider the second table in Exercise 2.52 on page 54 of the text (pg 52 abridged).

The data are the sales revenue ($m) for the different Business Groups within Woolworths Ltd for 1997 and 1998.

We will construct a component bar and a 100% component bar chart of this data in Excel.

Component Bar chart of the Sales Revenue of the Business Groups within Woolworths Ltd for

1997 and 1998

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

1997 1998

Year

Sal

es R

even

ue

($m

)

Wholesale

Special retail

General merchandise

Supermarkets

100% Component Bar Chart of the Sales Revenue of the Businsess Groups within

Woolworths Ltd for 1997 and 1998

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1997 1998

Year

Per

cen

tag

e o

f S

ales

R

even

ue Wholesale

Special retail

General merchandise

Supermarkets

Reading for next lecture

• Chapter 3 Sections 3.1-3.6