1. Describing data with graphics and numbers

2. Types of Data Categorical Variables –also known as class variables, nominal variables Quantitative Variables –aka numerical nariables –either continuous or discrete.

3. Graphing categorical variables

4. Ten most common causes of death in Americans between 15 and 19 years old in 1999.

5. Bar graphs

6. Graphing numerical variables

7. Heights of BIOL 300 students (cm) 165 168 163 173 170 163 170 155152 190 170 168 142 160 154 165156 177 173 165 165 175 155 166 168 165 180 165

8. Stem-and-leaf plot

9. 19 18 17 16 15 14 0 0 0 0 3 3 5 7 0 3 3 5 5 5 5 5 5 6 8 8 8 2 4 5 5 6 2

10. Frequency table Height GroupFrequency 141-150 151-160 161-170 171-180 181-190

11. Frequency table Height GroupFrequency 141-1501 151-1606 161-17015 171-1805 181-1901

12. Histogram

14. Frequency distribution

15. Histogram with more data

18. 90th percentile 50th percentile (median)

19. Associations between two categorical variables

20. Association between reproductive effort and avian malaria

22. Mosaic plot

23. Grouped Bar Graph

24. Associations between categorical and numerical variables

25. Multiple histograms

26. Associations between two numerical variables

27. Scatterplots

29. Evaluating Graphics Lie factor Chartjunk Efficiency

30. Don’t mislead with graphics

31. Better representation of truth

32. Lie Factor Lie factor = size of effect shown in graphic size of effect in data

33. Lie Factor Example Effect in graphic: 2.33/0.08 = 29.1 Effect in data: 6748/5844 = 1.15 Lie factor = 29.1 / 1.15 = 25.3

34. Chartjunk

36. Needless 3D Graphics

38. Summary: Graphical methods for frequency distributions

39. Summary: Associations between variables

40. Great book on graphics

41. Describing data

42. Two common descriptions of data Location (or central tendency) Width (or spread)

43. Measures of location Mean Median Mode

44. Mean n is the size of the sample

45. Mean Y 1 =56, Y 2 =72, Y 3 =18, Y 4 =42

46. Mean Y 1 =56, Y 2 =72, Y 3 =18, Y 4 =42 = (56+72+18+42) / 4 = 47

47. Median The median is the middle measurement in a set of ordered data.

48. The data: 18 28 24 25 36 14 34

49. The data: 18 28 24 25 36 14 34 can be put in order: 14 18 24 25 28 34 36 Median is 25.

51. Mean vs. median in politics 2004 U.S. Economy Republicans: times are good –Mean income increasing ~ 4% per year Democrats: times are bad –Median family income fell Why?

54. Measures of width Range Standard deviation Variance Coefficient of variation

55. Range 14 17 18 20 22 22 24 25 26 28 28 28 30 34 36

56. Range 14 17 18 20 22 22 24 25 26 28 28 28 30 34 36 The range is 36-14 = 22

58. Population Variance

59. Sample variance n is the sample size

60. Shortcut for calculating sample variance

61. Standard deviation (SD) Positive square root of the variance  is the true standard deviation s is the sample standard deviation

62. In class exercise Calculate the variance and standard deviation of a sample with the following data: 6, 1, 2

63. Answer Variance=7 Standard deviation =

64. Coefficient of variance (CV) CV = 100 s /.

65. Equal means, different variances

66. Manipulating means The mean of the sum of two variables: E[X + Y] = E[X]+ E[Y] The mean of the sum of a variable and a constant: E[X + c] = E[X]+ c The mean of a product of a variable and a constant: E[c X] = c E[X] The mean of a product of two variables: E[X Y] = E[X] E[Y] if and only if X and Y are independent.

67. Manipulating variance The variance of the sum of two variables: Var[X + Y] = Var[X]+ Var[Y] if and only if X and Y are independent. The variance of the sum of a variable and a constant: Var[X + c] = Var[X] The variance of a product of a variable and a constant: Var[c X] = c 2 Var[X]

68. Parents’ heights MeanVariance Father Height174.371.7 Mother Height160.458.3 Father Height +Mother Height 334.7184.9