Question

The following data are the joint temperatures of the O-rings (^oF) for each test firing or actual launch of the space shuttle rocket motor (from Presidential Commission on the Space Shuttle Challenger Accident, Vol. 1, pp. 129-131):

86

45

61

40

83

67

45

66

70

69

80

58

68

60

67

72

73

70

57

63

70

78

52

67

53

67

75

61

70

81

76

79

75

76

58

31

Round your answers to 2 decimal places (e.g. 98.76).

(a) Using the entire data, calculate the sample mean and sample standard deviation.

Sample mean =

Sample standard deviation =

(b) Remove the smallest observation (31°F) and calculate the sample mean and sample standard deviation of the remaining data.

Sample mean =

Sample standard deviation =

(c) With the smallest observation removed:

the sample mean Choose your answer; the sample mean ____ and the sample standard deviation Choose your answer; the sample standard deviation ______

Answer 1

a. Sample mean is

Create the following table.

data	data-mean	(data - mean)2
86	20.1944	407.81379136
45	-20.8056	432.87299136
61	-4.8056	23.09379136
40	-25.8056	665.92899136
83	17.1944	295.64739136
67	1.1944	1.42659136
45	-20.8056	432.87299136
66	0.1944	0.037791360000001
70	4.1944	17.59299136
69	3.1944	10.20419136
80	14.1944	201.48099136
58	-7.8056	60.92739136
68	2.1944	4.81539136
60	-5.8056	33.70499136
67	1.1944	1.42659136
72	6.1944	38.37059136
73	7.1944	51.75939136
70	4.1944	17.59299136
57	-8.8056	77.53859136
63	-2.8056	7.87139136
70	4.1944	17.59299136
78	12.1944	148.70339136
52	-13.8056	190.59459136
67	1.1944	1.42659136
53	-12.8056	163.98339136
67	1.1944	1.42659136
75	9.1944	84.53699136
61	-4.8056	23.09379136
70	4.1944	17.59299136
81	15.1944	230.86979136
76	10.1944	103.92579136
79	13.1944	174.09219136
75	9.1944	84.53699136
76	10.1944	103.92579136
58	-7.8056	60.92739136
31	-34.8056	1211.42979136

Find the sum of numbers in the last column to get.

So standard deviation is

b. Removing 31, we get sample mean as

Create the following table.

data	data-mean	(data - mean)2
86	19.2	368.64
45	-21.8	475.24
61	-5.8	33.64
40	-26.8	718.24
83	16.2	262.44
67	0.2	0.040000000000001
45	-21.8	475.24
66	-0.8	0.64
70	3.2	10.24
69	2.2	4.84
80	13.2	174.24
58	-8.8	77.44
68	1.2	1.44
60	-6.8	46.24
67	0.2	0.040000000000001
72	5.2	27.04
73	6.2	38.44
70	3.2	10.24
57	-9.8	96.04
63	-3.8	14.44
70	3.2	10.24
78	11.2	125.44
52	-14.8	219.04
67	0.2	0.040000000000001
53	-13.8	190.44
67	0.2	0.040000000000001
75	8.2	67.24
61	-5.8	33.64
70	3.2	10.24
81	14.2	201.64
76	9.2	84.64
79	12.2	148.84
75	8.2	67.24
76	9.2	84.64
58	-8.8	77.44

Find the sum of numbers in the last column to get.

So standard deviation is

c. With the smallest observation removed: the sample mean increased and the sample standard deviation decreased.