1. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. SSF1063: Statistics for Social Sciences LU2: Graphing Qualitative and Quantitative Data 14 th January 2008

2. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.1 (p. 27) Ages of 50 Students What can you make out from this set of data? Is it easy to read? What does it mean to you?

3. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.3 (p. 28) Type of Employment Students Intend to Engage In The frequency table (shown above) displays how the frequencies are distributed over various categories.

4. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Example 2-1 (p. 28) A sample of 30 employees were asked how stressful their job were. Their responses are recorded below where VS represents very stressful, SS means somewhat stressful and N for not stressful at all. SSNSSVSVSN VSSSSSVSSSSS VSSSNVSNSS SSVSSSSSVSN SSVSVSSSNSS

5. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.4 (p. 29) Frequency Distribution of Stress on Job

6. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.5 (p. 29) Relative Frequency and Percentage Distributions of Stress on Job Relative Frequency of a category = Frequency of that category Sum of all frequencies *To explain proportion of frequency belongs to the correspond category

7. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Case Study 2.1 (p. 30) Marrying in the USA Source: USA TODAY, November 10, 2003. Copyright © 2003, USA TODAY. Chart reproduced with permission Try this… Using the information shown in bar graph, construct a frequency table, calculate the relative frequencies and percentages.

8. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. ‘A picture is worth a thousand words’ Why do we need to display our data graphically? –Because it reveals the main characteristics of the data set at a glance –The two types of graphs commonly use to display qualitative data are: Bar graph Pie chart Graphical Presentation of Qualitative Data

9. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.1 (p. 30) Bar graph for the frequency distribution of Table 2.4. Bar graphs Mark various categories on the horizontal axis Categories are represented by interval same width Height of the bar corresponds with the frequency of each category A small gap between bars

10. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Case Study 2.2 (p. 31) Americans Say Keep the Penny. Do You Favor Abolishing the Penny? Pie Charts A circle divided into portions that represent the relative frequencies or percentages of a population or a sample belonging to different categories.

11. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.6 (p. 31) Calculating Angle Sizes for the Pie Chart

12. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.2 (p. 32) Pie chart for the percentage distribution of Table 2.5.

13. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. This section shows you how to group and display quantitative data. We begin with the subtopic Frequency Distribution Organizing And Graphing Quantitative Data

14. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.7 (p. 34): Frequency distribution table Weekly Earnings of 100 Employees of a Company *Make sure the classes are not overlapping!

15. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Remember last week we discussed that continuous data is any numerical values over certain intervals; that it may have decimals? So, where do we put 800.7 or 1200.5? This is when you need to determine the class boundaries. –The class boundary is a midpoint that cuts the upper limit of one class and the lower limit of the next class Organizing And Graphing Quantitative Data: Frequency Distribution (1)

16. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. The difference between the two boundaries of a class gives the class width. Class width is also known as the class size. Class width = Upper boundary – Lower boundary or; = (Upper limit – Lower limit) + 1 The class midpoint is obtained by dividing the sum of the two limits of a class by 2. Class midpoint = Lower limit + Upper limit 2 Organizing And Graphing Quantitative Data: Frequency Distribution (2)

17. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.8 (p. 35) Class Boundaries, Class Widths, and Class Midpoints for Table 2.7

18. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Involves 3 major consideration: –Number of classes –Class width –Lower Limit of the First Class or the Starting Point Constructing Frequency Tables

19. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.9 (p. 37) Home Runs Hit by Major League Baseball Teams During the 2004 Season

20. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.10 (p. 37) Frequency Distribution for the Data of Table 2.9

21. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.11 (p. 38) Relative Frequency and Percentage Distributions for Table 2.10 What conclusions you can make from Table 2.11 above?

22. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Histogram –Bars that are constructed adjacent to each other to represent frequencies, relative frequencies or percentages; marked by the height of the bars –What is the difference between an ordinary bar graph with a histogram? –Explain why the bars need to be constructed next to each other without gaps? Graphing Grouped Data

23. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.3 (p. 39) Frequency histogram for Table 2.10.

24. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Case Study 2.3 (p. 40) Hand Hygiene Source: USA TODAY, December 14, 2004. Copyriht © 2004, USA TODAY. Chart reproduced with permission.

25. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.5 (p. 41) Frequency polygon for Table 2.10 Polygon – constructed by joining midpoints of bars in a histogram with straight lines

26. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.6 (p. 41) Frequency distribution curve. As number of classes increased followed by decreased class width, the frequency polygon becomes a smooth curve; known as the Frequency Distribution Curve.

27. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.13 (p. 43) Frequency Distribution of Vehicles Owned Example of Frequency table for single valued classes

28. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.7 (p. 44) Bar graph for Table 2.13.

29. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Case Study 2.4 (p. 44) USA Is a Caffeinated Country Source: USA TODAY, April 13, 2005. Copyriht © 2005, USA TODAY. Chart reproduced with permission

30. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.8 (p. 45) Symmetric histograms. Shapes of Histograms (1)

31. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.9 (p. 45) (a) A histogram skewed to the right. (b) A histogram skewed to the left. Shapes of Histograms (2)

32. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.10 (p. 45) A histogram with uniform distribution. Shapes of Histograms (3)

33. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Case Study 2.5 (p. 46) Using Truncated Axes Are the two graphs similar?

34. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.11 (p. 46) (a) and (b) Symmetric frequency curves. (c) Frequency curve skewed to the right. (d) Frequency curve skewed to the left.

35. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Ogives –A curve drawn by joining the dots marked above the upper boundaries of classes using a straight line –Similar lower boundary for all classes, with different upper boundaries –“How many students eat FOUR plates of rice and less in a day?” Cumulative Frequency Distributions

36. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.14 (p. 52) Cumulative Frequency Distribution of Home Runs by Baseball Teams

37. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Table 2.15 (p. 53) Cumulative Relative Frequency and Cumulative Percentage Distributions for Home Runs Hit by Baseball Teams

38. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.12 (p. 53) Ogive for the cumulative frequency distribution of Table 2.14 16 baseball teams had 188 or fewer home runs during the 2004 season

39. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.13 (p. 55) Stem-and-leaf display. Stem-and-Leaves Display

40. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.14 (p. 56) Stem-and-leaf display of test scores.

41. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.15 (p. 56) Ranked stem-and-leaf display of test scores.

42. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.16 (p. 56) Stem-and-leaf display of rents.

43. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.17 (p. 57) Grouped stem-and-leaf display.

44. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.21 (p. 62) Histogram of the Ages of Company X’s Workers.

45. Prem Mann, Introductory Statistics, 6/E Copyright  2007 John Wiley & Sons. All rights reserved. Figure 2.22 (p. 62) Histogram of the Ages of Company X’s Workers.