1. GRAPHICAL DESCRIPTIVE STATISTICS FOR QUALITATIVE, TIME SERIES AND RELATIONAL DATA

2. Reasons To Collect Data Obtain Input to a Research Study Measure Performance Assist in Formulating Decision Alternatives Satisfy Curiosity –Knowledge for the Sake of Knowledge

3. Random Variables Random variables are phenomena or characteristics that are not known in advance Data are observations of random variables

4. TYPES OF DATA Qualitative –Result to a survey question is non-numeric Categorical Data Ordinal (Ranked) Data Quantitative –Result to a survey question is a number Ratio Data – Has an “absolute 0” point, e.g. age Interval – 0 is simply another number – e.g. degrees Fahrenheit

5. Graphical Techniques Qualitative Data Pie Charts Bar Charts

6. Plot of Frequency Distributions Objective is to develop a frequency distribution table –Hand Count –Excel Approach COUNTIF command

7. Pie Charts Determine the relative frequency for each category Apportion sectors (wedges) of a 360 degree circle proportionately

8. Example Frequency Distribution of Origin of Car Manufacturer Frequency American16 Asian20 European 4 Relative Frequency.40.50.10

9. Pie Chart

10. Bar Charts Bars show the frequency or relative frequency of the observations Consider the same example

11. Frequency Bar Chart

12. Relative Frequency Bar Chart

13. EXCEL Pie Charts Example -- 66 people surveyed and asked the color of their car -- Their choices: –Red –Blue –Black –White –Other These are recorded in cells A2 to A67 of a spreadsheet

14. Determining Frequency Distributions Step 1 – Record Responses in a Column Record responses recorded in column A

15. Step 2 – Type Categories in another Column Type Categories in Column B

16. Step 3 – Use COUNTIF to Determine Frequencies =COUNTIF( ) Drag down to C3:C6 What it should match (Relative Address)B2 Where data is located (Drag down)$A$2:$A$67,

17. 1. Go to Chart Wizard 2. Select Pie Creating a Pie Chart 3. Select this sub-type Click Next

18. Creating a Pie Chart - 2 Highlight Cells B1through C6 First Column – Labels Second Column -- Frequencies Click Next

19. Creating a Pie Chart - 3 1. Put in an appropriate title 2. Click Legend Tab

20. Creating a Pie Chart - 4 1. Uncheck Show legend 2. Click Data Labels Tab

21. Creating a Pie Chart - 5 Put bullet in Show label and percent Click Finish

22. Completed Pie Chart

23. Editing Options Enlarge Put Labels Inside Wedges Change Colors Add Text Etc.

24. EXCEL Bar Charts What we call Bar Charts, Excel calls Column Charts –The steps are similar If you already have a pie chart, you can convert it to a bar chart as shown on the next slide:

25. Creating a Bar Chart From a Pie Chart 1. 1.Right Mouse Click on graph 2. 2.Select Chart Type 3. Select Column

26. Resulting Bar Chart

27. Line Charts for Time Series Data Time series -- Values vs. time –Dow Jones vs. Day –Sales vs. Quarter –Population vs. Year Typically depicted as line charts In Excel if you already have a bar chart you can convert it to a line chart using the method on the last slide –Otherwise we do the following

28. Example -- Sales at Epencil.com 1. Go to Chart Wizard 2. Select Line Click Next

29. 1. Enter Cells with With Sales Figures B2:B8 2. Click Series Tab

30. 1. Enter Chart Title 2. Enter Years Cells A2:A8 Click Next

31. Note: In this dialogue box, there are many editing features 2. Enter a label for Y-axis 1. Enter a label for X-axis 3. Click Legend Tab

32. 1. Uncheck Show legend 2. Click Finish

33. Can now edit figure: Resize Delete Gray Background Delete Lines Etc.

34. Scatter Diagrams -- Showing Relationships Between Variables A scatter diagram shows the relationship between two quantitative variables as a plot of a series of points (observations) –(Grade vs. Study time) –(Sales vs. Advertising $) –(Production vs. Resources) Types of relations that can be detected –Linear (Positive or Negative) Least Squares Line -- “Best” line through points –Nonlinear –No Relation

35. Example Sales of Pencils at Epencil vs. Advertising $ spent during the week

36. 1. Click Chart Wizard 2. Select Scatter Click Next

37. 1. Enter data columns for both X and Y with the column for X first. Do not include the labels. 2. Click Series Tab

38. Enter Chart Title Click Next

39. In this dialogue box there are many editing features 1. Uncheck Show legend 2. Click Titles Tab

40. 1. Enter X-axis Label 2. Enter Y-axis Label Click Finish

41. Can now edit figure: Resize Delete Gray Background Delete Lines Etc.

42. Determining Trend We can have Excel put the best straight line or other curve (parabola, etc.) through these points so that we can easily observe trend

43. 1. Right mouse click on any data point so that squares appear in the data points 2. Select Add Trendline from the Popup Menu 3. Select Type (Usually Linear)

44. Trendline added

45. How to Lie With Statistics Graphs can be used to accurately portray data However, sometimes a graph can be distorted in such a way as to skew the information it conveys Examples –Fatter or different shaped bars –Stretched or condensed axes –No indication of a “break” on the axis –Unlabeled axes

46. Review How to construct by hand and by Excel –Pie Charts for Qualitative Data –Bar Charts for Qualitative Data –Line Charts for Time Series Data –Scatter Diagrams to Show Relationships Between Variables How Graphs Can be Deceptive