1. SECTION 2.1 GRAPHICAL SUMMARIES FOR QUALITATIVE DATA Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2. Section 2.1 - Objectives 1. Construct frequency distributions for qualitative data 2. Construct bar charts 3. Construct pie charts Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

3. Construct frequency distributions for qualitative data Objective 1 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

4. Frequency Distribution The frequency of a category is the number of times it occurs in the data set. A frequency distribution is a table that presents the frequency for each category. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

5. Example 2.1 A computer retailer compiles a list of the types of computers sold to the last 50 customers. To construct a frequency distribution, we begin by tallying the number of observations in each category. TabletLaptop NotebookDesktopLaptop NotebookDesktopLaptop Notebook DesktopLaptop DesktopLaptopTabletNotebookTablet Notebook TabletLaptopDesktop Laptop Desktop NotebookLaptopDesktopLaptop DesktopTabletDesktopLaptop DesktopTabletNotebookTabletLaptop Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

6. Solution Then we record the totals for each of the types of computers. Type of ComputerFrequency Desktop11 Laptop23 Notebook9 Tablet7 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

7. Relative Frequency Distribution A frequency distribution makes it easy to see exactly how many observations are in each category. Sometimes we are interested in the proportion of observations in each category. The proportion of observations in a category is called the relative frequency of the category. A relative frequency distribution is a table that presents the relative frequency for each category Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

8. Computing Relative Frequencies The relative frequency of a category is the frequency of the category divided by the sum of all the frequencies. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

9. Example 2.2 Construct a relative frequency distribution for the computer sales data. Type of ComputerFrequency Desktop11 Laptop23 Notebook9 Tablet7 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

10. Solution We begin by finding the total number of observations by summing the frequencies: 11 + 23 + 9 + 7 = 50 Next, we compute the relative frequency for each type of computer: Type of ComputerFrequencyRelative Frequency Desktop1111/50 = 0.22 Laptop2323/50 = 0.46 Notebook99/50 = 0.18 Tablet77/50 = 0.14 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

11. Construct bar graphs Objective 2 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

12. Bar Graphs A bar graph is a graphical representation of a frequency distribution. A bar chart consists of rectangles of equal width, with one rectangle for each category. The heights of the rectangles represent the frequencies or relative frequencies of the categories. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

13. Example 2.3 Construct a frequency bar graph and the relative frequency bar graph for the computer sales data. Type of ComputerFrequencyRelative Frequency Desktop110.22 Laptop230.46 Notebook90.18 Tablet70.14 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14. Solution Type of ComputerFrequencyRelative Frequency Desktop110.22 Laptop230.46 Notebook90.18 Tablet70.14 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

15. Pareto Chart Sometimes it is desirable to construct a bar graph in which the categories are presented in order of frequency, with the largest frequency on the left and the smallest frequency on the right. This type of graph is called a Pareto chart. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

16. Example 2.4 Construct a relative frequency Pareto Chart for the computer sales data presented in the table below. Type of ComputerFrequencyRelative Frequency Desktop110.22 Laptop230.46 Notebook90.18 Tablet70.14 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

17. Solution Type of ComputerFrequencyRelative Frequency Desktop110.22 Laptop230.46 Notebook90.18 Tablet70.14 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

18. Horizontal Bars The bars in a bar graph may be either horizontal or vertical. Horizontal bars are sometimes more convenient when the categories have long names. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

19. Example 2.5 Type of employmentRelative Frequency Farming, forestry, fishing 0.007 Manufacturing, extraction, transportation and crafts 0.203 Managerial, professional, technical 0.373 Sales and Office 0.242 Other Services 0.176 Source: CIA – The World Factbook Following is the relative frequency distribution categorizes employed U.S. residents by type of employment in the year 2009. Construct a relative frequency bar graph. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

20. Solution Type of employmentRelative Frequency Farming, forestry, fishing 0.007 Manufacturing, extraction, transportation and crafts 0.203 Managerial, professional, technical 0.373 Sales and Office 0.242 Other Services 0.176 Source: CIA – The World Factbook Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

21. Side-by-Side Bar Graphs Sometimes we want to compare two bar charts that have the same categories. The best way to do this is to construct both bar charts on the same axes, putting bars that correspond to the same category next to each other. This is called a side- by-side bar graph. The following example presents the number of visitors, in millions, to several popular websites in February 2009 and in February 2010. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

22. Example – Side-by-Side Bar Graph Website February 2009 February 2010 Facebook 65125 Google 126137 YouTube 7093 Microsoft Network (MSN) 3738 Yahoo 66 Source: mostpopularwebsites.net Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

23. Construct pie charts Objective 3 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

24. Pie Chart A pie chart is an alternative to the bar chart for displaying relative frequency information. A pie chart is a circle. The circle is divided into sectors, one for each category. The relative sizes of the sectors match the relative frequencies of the categories. For example, if a category has a relative frequency of 0.25, then its sector takes up 25% of the circle. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

25. Example 2.6 Construct a pie chart for the computer sales data. Type of ComputerRelative Frequency Desktop0.22 Laptop0.46 Notebook0.18 Tablet0.14 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

26. Do You Know… How to construct a frequency and relative frequency distribution for qualitative data? How to construct the various kinds of bar graphs? How to construct a pie chart? Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.