1. QBM117 Business Statistics Descriptive Statistics Graphical Presentation of Qualitative Data

2. Objective To summarise qualitative data using pie charts and bar charts

3. 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.

4. 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.

5. Area of EmploymentNumber of Graduates Accounting73 Finance52 General Management36 Marketing64 Other28 Total253

6. 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.

7. 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.

8. Example 2.3 revisited Construct a pie chart of the data. Area of EmploymentNumber of Graduates Accounting73 Finance52 General Management36 Marketing64 Other28 Total253

9. Employment Area Number of Graduates Proportion of Graduates Angle of Circle Accounting7373/253=0.28850.2885x360°=104° Finance5252/253=0.20550.2055x360°=74° Management3636/253=0.14230.1423x360°=51° Marketing6464/253=0.25300.2530x360°=91° Other2828/253=0.11070.1107x360°=40° Total2531.0000360°

11. 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.

12. 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.

13. Example 2.3 revisited Construct a bar chart of the data. Area of EmploymentNumber of Graduates Accounting73 Finance52 General Management36 Marketing64 Other28 Total253

15. 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.

16. 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.

19. 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.

20. 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.

21. 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.

23. 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.

26. Reading for next lecture Chapter 3 Sections 3.1-3.6