Question

A physiological experiment was concluded to study the effect of various factors on a pulse rate. The participants took their own pulse. They then were asked to flip a coin. If their coin came up head, they were to run in place for 1 minute. Then everyone took their own pulse again. The dataset pulse.txt, available from Moodle, contains the following variables: ROW- id numbers, from 1 to 92; PULSE1- first pulse rate; PULSE2- second pulse rate; RAN-1=ran in place, 2 =did not run; SMOKES-1=smokes regularly, 2=does not smoke regularly; SEX-1=male, 2=female; HEIGHT-height in inches; WEIGHT-weight in pounds; ACTIVITY-usual level of physical activity: 1=slight, 2=moderate, 3=a lot.

Use this data for the following questions.

(a) Find the histograms for pulse2, weight and height; Are they symmetrically distributed?

(b) Find the sample mean and sample standard deviation for pulse1.

(c) Construct a scatter plot between weight and height, categorized by male and female. What pattern have you observed?

Pulse data set

1 64 88 1 2 1 66.00 140 2

2 58 70 1 2 1 72.00 145 2

3 62 76 1 1 1 73.50 160 3

4 66 78 1 1 1 73.00 190 1

5 64 80 1 2 1 69.00 155 2

6 74 84 1 2 1 73.00 165 1

7 84 84 1 2 1 72.00 150 3

8 68 72 1 2 1 74.00 190 2

9 62 75 1 2 1 72.00 195 2

10 76 118 1 2 1 71.00 138 2

11 90 94 1 1 1 74.00 160 1

12 80 96 1 2 1 72.00 155 2

13 92 84 1 1 1 70.00 153 3

14 68 76 1 2 1 67.00 145 2

15 60 76 1 2 1 71.00 170 3

16 62 58 1 2 1 72.00 175 3

17 66 82 1 1 1 69.00 175 2

18 70 72 1 1 1 73.00 170 3

19 68 76 1 1 1 74.00 180 2

20 72 80 1 2 1 66.00 135 3

21 70 106 1 2 1 71.00 170 2

22 74 76 1 2 1 70.00 157 2

23 66 102 1 2 1 70.00 130 2

24 70 94 1 1 1 75.00 185 2

25 96 140 1 2 2 61.00 140 2

26 62 100 1 2 2 66.00 120 2

27 78 104 1 1 2 68.00 130 2

28 82 100 1 2 2 68.00 138 2

29 100 115 1 1 2 63.00 121 2

30 68 112 1 2 2 70.00 125 2

31 96 116 1 2 2 68.00 116 2

32 78 118 1 2 2 69.00 145 2

33 88 110 1 1 2 69.00 150 2

34 62 98 1 1 2 62.75 112 2

35 80 128 1 2 2 68.00 125 2

36 62 62 2 2 1 74.00 190 1

37 60 62 2 2 1 71.00 155 2

38 72 74 2 1 1 69.00 170 2

39 62 66 2 2 1 70.00 155 2

40 76 76 2 2 1 72.00 215 2

41 68 66 2 1 1 67.00 150 2

42 54 56 2 1 1 69.00 145 2

43 74 70 2 2 1 73.00 155 3

44 74 74 2 2 1 73.00 155 2

45 68 68 2 2 1 71.00 150 3

46 72 74 2 1 1 68.00 155 3

47 68 64 2 2 1 69.50 150 3

48 82 84 2 1 1 73.00 180 2

49 64 62 2 2 1 75.00 160 3

50 58 58 2 2 1 66.00 135 3

51 54 50 2 2 1 69.00 160 2

52 70 62 2 1 1 66.00 130 2

53 62 68 2 1 1 73.00 155 2

54 48 54 2 1 1 68.00 150 0

55 76 76 2 2 1 74.00 148 3

56 88 84 2 2 1 73.50 155 2

57 70 70 2 2 1 70.00 150 2

58 90 88 2 1 1 67.00 140 2

59 78 76 2 2 1 72.00 180 3

60 70 66 2 1 1 75.00 190 2

61 90 90 2 2 1 68.00 145 1

62 92 94 2 1 1 69.00 150 2

63 60 70 2 1 1 71.50 164 2

64 72 70 2 2 1 71.00 140 2

65 68 68 2 2 1 72.00 142 3

66 84 84 2 2 1 69.00 136 2

67 74 76 2 2 1 67.00 123 2

68 68 66 2 2 1 68.00 155 2

69 84 84 2 2 2 66.00 130 2

70 61 70 2 2 2 65.50 120 2

71 64 60 2 2 2 66.00 130 3

72 94 92 2 1 2 62.00 131 2

73 60 66 2 2 2 62.00 120 2

74 72 70 2 2 2 63.00 118 2

75 58 56 2 2 2 67.00 125 2

76 88 74 2 1 2 65.00 135 2

77 66 72 2 2 2 66.00 125 2

78 84 80 2 2 2 65.00 118 1

79 62 66 2 2 2 65.00 122 3

80 66 76 2 2 2 65.00 115 2

81 80 74 2 2 2 64.00 102 2

82 78 78 2 2 2 67.00 115 2

83 68 68 2 2 2 69.00 150 2

84 72 68 2 2 2 68.00 110 2

85 82 80 2 2 2 63.00 116 1

86 76 76 2 1 2 62.00 108 3

87 87 84 2 2 2 63.00 95 3

88 90 92 2 1 2 64.00 125 1

89 78 80 2 2 2 68.00 133 1

90 68 68 2 2 2 62.00 110 2

91 86 84 2 2 2 67.00 150 3

92 76 76 2 2 2 61.75 108 2

Answer 1

1. i) The histogram for the pluse 2 is given by and it is not symmetric. From the graph it shown as positively skewed.

ii) ) The histogram for the height is given by and it is not symmetric, it is negatively skewed.

iii) The histogram for the weight is given by and it is not symmetric, it is positively skewed.

B)

Descriptives
	Mean	Standard Deviation
pluse1	72.87	11.009

The sample mean for the mean is 72.87 and standard deviation 11.009

C) The scatter plot between weight and height, categorized by male and female is given by.

Conclusion: here 1= male and 2= female, and we observe relationship between height and weight is positively correlated. That means as height increases the weight also increases.