1. Chapter 2 Presenting Data in Tables and Charts

2. Note: Sections 2.1 & 2.2 - examining data from 1 numerical variable. Section 2.3 - examining data from 2 numerical variables. Section 2.4 - examining data from 1 categorical variable (read). Section 2.5 - examining data from 2 categorical variables.

3. Section 2.1 Organizing Numerical Data Examining One Numerical Variable.

4. Ordered Array Array of data ordered from smallest to largest value –Makes it easier to see the extreme values and where the majority of values are located.

5. Using Excel Data | Sort Select the heading of the column you want to sort by first. Choose ascending or descending. Select the heading of the column you wanted to sort by second. Choose ascending or descending. Etc. Choose appropriate button “Header row” or “No header row”.

6. Stem & Leaf Display Shows how the data varies over a range of observations Separates data according to leading digits (stems) and trailing digits (leaves).

7. Stem & Leaf Display Stem Unit of 1 743 6 75 76 77 784 798 802 814 82 83 847 85 86 88 892

8. Stem & Leaf Display x 74 5 8 80 0 1 5 9 The 10 in the top right cell shows that the number rounds to 80 but is in the 70’s

9. Using PHStat to create a Stem & Leaf Display PHStat | Descriptive Statistics | Stem-and-Leaf Display Enter range of values If selection contains a heading, leave selected “First cell contains a label”. Select Stem Unit Enter Title

10. Section 2.2 Tables And Charts For Numerical Data Examining One Numerical Variable

11. The Frequency Distribution Data is arranged into class groupings. Creating class groupings –Number of classes Depends on number of observations Typically 5 <= class groupings < 15 –Intervals should be the same width. Use the following: Width of interval = Range / Number of class groupings –Avoid overlapping classes

12. Frequency Distribution (continued) Consists of the number of occurrences of a value fitting within the range of each interval. Advantage - Data characteristics can be approximated. Disadvantage - Individual values are lost due to the grouping.

13. Ex. Given the following data: 74 74.3 74.6 78.4 79.8 80.2 81.4 82.0 84.7 86.0 89.2 Number of classes. Width of interval Lets choose 589.2 - 74 = 3.04 5 Approx. 3

14. Frequency Distribution IntervalFrequency 74 - 773 77 - 802 80 - 833 83 - 861 86 - 891 89 - 921 Right boundary is not included.

15. Using PHStat to create a Frequency Distribution PHStat | Descriptive Statistics | Frequency Distribution Enter the variable cell range Enter the bin cell range If you selected the heading when selecting the data, leave selected “First cell in each range contains label”. Leave selected “Single Group Variable” Enter title of your choice.

16. Bin (Used for PHStat only) Contains the values that approximate the maximum value of each class. For example: –If your intervals are, -20.0 to -10.0 -10.0 to 0.0 0 to 10.0 10.0 to 20.0 –Your bin values could be -10.1 -0.1 9.9 19.9

17. Bin Values Intervals

18. If your data were recorded with 2 places after the decimal, your bin values would be: -10.01 -.01 9.99 19.99

19. Example See the file Sec2.2.xls

20. Relative Frequency Distribution First create a Frequency Distribution. The values in the Relative Frequency Distribution are formed by dividing the frequency of each value within each class by the total number of values. The Relative Frequency Distribution contains the proportion of times a value occurs within each class.

21. Relative Frequency Distribution IntervalFrequencyRelative Frequency 74 - 7733/11 =.2727 77 - 8022/11 =.1818 80 - 8333/11 =.2727 83 - 8611/11 =.0909 86 - 8911/11 =.0909 89 - 9211/11 =.0909 Total11

22. Percentage Distribution First create a Relative Frequency Distribution The values in the Percentage Distribution are formed by multiplying each proportion in the Rel. Freq. Dist. by 100.

23. Percentage Distribution IntervalFreq.Rel. Freq.Percentage Freq. 0 - 7400.000% 74 - 773.272727.27% 77 - 802.181818.18% 80 - 833.272727.27% 83 - 861.09099.09% 86 - 891.09099.09% 89 - 921.09099.09% Total11

24. Benefit of a Relative Frequency Distribution or Percentage Distribution Essential when comparing two sets of data consisting of a different number of values.

25. For example: 2 5 8 2 9 2 5 2 8 5 5 5 8 5 2 5 5 Study 2Study 1 5 occurs 7/12 times. 7/12 = 0.583 Or 58.3% of the time 5 occurs 1/5 times. 1/5 = 0.2 Or 20% of the time

26. Cumulative Percentage Distribution Demonstrates the growth over the classes.

27. Cumulative Percentage Distribution IntervalRel.Fq.Cumulative Dist. 0 - 740.000% = 0.0% 74 - 770.27270% = 0.0% 77 - 800.181827.27% = 27.27% 80 - 830.272727.27% + 18.18% = 45.45% 83 - 860.090927.27% + 18.18% + 27.27% = 72.72% 86 - 890.090927.27% + 18.18% + 27.27% 9.09% =81.81% 89 - 920.090927.27% + 18.18% + 27.27% + 9.09% + 9.09% = 90.9% 92 - 950.0027.27% + 18.18% + 27.27% + 9.09% + 9.09% + 9.09% = 99.99% Total.9999

28. Cumulative Percentage Distribution Top of Pg. 56. SOLUTION From Table 2.5... Error

29. Using PHStat to create a Percentage or Cumulative Percentage Distribution These are automatically generated when you create a Frequency distribution.

30. Class Midpoint Point halfway between the boundaries of each class.

31. Histogram Using a picture to demonstrate data. Describes the numerical data that has been grouped into a frequency, relative frequency, or percentage distribution. The random variable of interest is displayed along the horizontal axis (x-axis). The number, proportion or percentage of values per class are plotted along the vertical axis (y-axis)

32. Histogram

33. Polygon (same info as Histogram) Using a picture to demonstrate data. Describes the numerical data that has been grouped into a frequency, relative frequency, or percentage distribution. The random variable of interest is displayed along the horizontal axis (x-axis). The number, proportion or percentage of values per class are plotted along the vertical axis (y-axis)

34. Polygon

35. Using PHStat to create a Histogram & Polygon PHStat | Descriptive Statistics | Histogram & Polygons Enter the Variable Cell Range Enter the Bin Cell Range Enter the Midpoints Cell Range If the first row contains headings, leave selected “First cell in each range contains label”. Select “Multiple Groups - Unstacked”. Enter title of your choice Leave check boxes on default selection.

36. Section 2.3 Graphing Bivariate Numerical Data Examining 2 numerical variables.

37. Scatter Diagram Used to demonstrate the relationship between to numerical variables. One numerical variable is plotted on the x-axis. The other numerical variable is plotted on the y-axis. The result is a point on the x-y plane.

38. Example Cholesterol Level Meat Consumption in Ounces / Day 200176115100120199151100150 24218333026615

39. Scatter Diagram of previous data: Cholesterol Level

40. Section 2.4 Tables and charts for categorical data Covered in CSC 199 –Read

41. Section 2.5 Tabulating and Graphing Bivariate Categorical Data Use a Contingency Table or a Side-By-Side Chart.

42. Contingency Table Also called, “Cross-Classification Table” Used to study the values from two categorical variables.

43. Example: A sample of 20 graduates was taken and each individual was asked: 1. What was your major? 2. What is your salary level? = $50,000 DegreeYear in School English >=$50,000 Math $30,000 - $50,000 Math <= $30,000 English $30,000 - $50,000 English <= $30,000 Philosophy $30,000 - $50,000 Philosophy <= $30,000 English >=$50,000 Philosophy <= $30,000 Math >=$50,000 Math $30,000 - $50,000 Math >=$50,000 Math >=$50,000 English $30,000 - $50,000

44. A count of the number of degrees within each salary range. Degree<= $30,000$30,000 - $50,000>= $50,000Total English1225 Math1236 Philosophy2103 Grand Total45514 Percentages based on overall total Degree<= $30,000$30,000 - $50,000>= $50,000Total English7.14%14.29% 35.71% Math7.14%14.29%21.43%42.86% Philosophy14.29%7.14%0.0%21.43% Total28.57%35.71% 100.00% Each value is divided by the total (12)

45. 28.57 % of all polled make $30,000 or under. 42.86 % of all polled majored in math. 21.43 % of all polled majored in math and make $50,000 or more. Percentages based on overall total Degree<= $30,000$30,000 - $50,000>= $50,000Total English7.14 %14.29 % 35.71 % Math7.14 %14.29 %21.43 %42.86 % Philosophy14.29 %7.14 %0.0 %21.43 % Total28.57 %35.71 % 100.00 %

46. Percentages based on row total Degree<= $30,000$30,000 - $50,000>= $50,000Total English20.00 %40.00 % 100.00 % Math16.67 %33.33 %50.00 %100.00 % Philosophy66.67 %33.33 %0.0 %100.00 % Total28.57 %35.71 % 100.00 % Each value is divided by the total of its row. A count of the number of degrees within each salary range. Degree<= $30,000$30,000 - $50,000>= $50,000Total English1225 Math1236 Philosophy2103 Grand Total45514

47. Percentages based on row total Degree<= $30,000$30,000 - $50,000>= $50,000Total English20.00 %40.00 % 100.00 % Math16.67 %33.33 %50.00 %100.00 % Philosophy66.67 %33.33 %0.0 %100.00 % Total28.57 %35.71 % 100.00 % Of those who majored in math, 50.00 % make $50,000 or more. Of those who majored in philosophy, 66.67 % make $30,000 or less.

48. Percentages based on column total Degree<= $30,000$30,000 - $50,000>= $50,000Total English25.00 %40.00 % 35.71 % Math25.00 %40.00 %60.00 %42.86 % Philosophy50.00 %20.00 %0.0 %21.43 % Total100.00 % Each value is divided by the total of its column A count of the number of degrees within each salary range. Degree<= $30,000$30,000 - $50,000>= $50,000Total English1225 Math1236 Philosophy2103 Grand Total45514

49. Percentages based on column total Degree<= $30,000$30,000 - $50,000>= $50,000Total English25.00 %40.00 % 35.71 % Math25.00 %40.00 %60.00 %42.86 % Philosophy50.00 %20.00 %0.0 %21.43 % Total100.00 % Of those who make $30,000 or less, 50.00 % majored in philosophy Of those who make between $30,000 and $50,000, 20.00 % majored in philosophy.

50. Side-By-Side Chart Visual display of bivariate categorical data. Used to detect relationships in the data.

51. Consider the following data: NCSCNEIL Percentage of Pop. that is literate93899998 Percent of crime-related deaths101545

52. Side-By-Side Chart of the previous data

53. See the following: Excel Handbook for Chapter 2 Pg. 93 - 104