Many standard statistical methods that you will study in Part II of this book ar

Question

Many standard statistical methods that you will study in Part II of this book are intended for use with distributions that are symmetric and have no outliers. These methods start with the mean and standard deviation, x and s. For example, standard methods would typically be used for the IQ and GPA data here data449.dat.

(a) Find x and s for the IQ data. (Round your answers to two decimal places.)

(b) Find the median IQ score. It is, as we expect, close to the mean.
3

(c) Find the mean and median for the GPA data. The two measures of center differ a bit. (Round your answers to two decimal places.)

What feature of the data (make a stemplot or histogram to see) explains the difference?

obs gpa iq gender concept 1 7.84 82 2 67 2 9.3 82 2 43 3 6.24 129 2 52 4 6.4 106 2 66 5 10.96 115 1 58 6 9 81 2 51 7 8.51 99 2 71 8 10.02 79 2 51 9 6.74 98 1 49 10 10.02 106 2 51 11 10.69 107 1 35 12 2.31 122 1 54 13 2.64 103 2 54 14 8.87 90 1 64 15 7.09 82 1 56 16 8.39 135 1 69 17 8.02 106 1 55 18 9.7 104 1 65 19 9.33 108 2 40 20 10 122 1 66 21 5.94 88 2 55 22 9.59 101 2 20 24 8.53 91 1 56 26 8.64 105 2 68 27 9.25 66 1 69 28 10.6 95 2 70 29 7.85 80 2 80 30 8.19 115 2 53 31 9.58 111 2 65 32 9.69 115 1 67 33 2.1 80 1 62 34 10.85 97 1 39 35 10.66 94 2 71 36 10.85 100 2 59 37 10.22 98 1 60 38 7.28 127 2 64 39 7.14 96 2 71 40 10.42 109 1 72 41 8.81 112 1 54 43 10.66 95 2 64 44 7.08 80 2 58 45 6.06 105 2 70 46 7.57 101 2 72 47 9.93 99 2 70 48 6.65 56 2 47 50 5.21 108 2 52 51 9.66 93 1 46 52 10.15 83 2 66 53 9.26 92 2 67 54 8.61 81 2 63 55 8.73 91 2 53 56 10.2 87 2 67 57 7.91 119 2 61 58 7.84 93 1 54 59 7.47 96 1 60 60 9.58 100 1 60 61 10.73 83 2 63 62 9.48 113 2 30 63 9.88 109 2 54 64 8.82 105 2 66 65 4.21 132 2 44 68 10.95 82 2 49 69 10.56 121 1 44 71 8.84 106 2 67 72 9.12 93 1 64 74 5.94 102 2 73 76 6.53 109 2 59 77 7.46 120 1 37 78 10.88 107 1 63 79 4.08 120 2 36 80 10.06 111 1 64 83 10.91 113 2 42 84 5.25 104 1 28 85 4.62 99 1 60 86 7.82 112 1 70 87 6.94 104 2 51 88 9.94 111 1 21 89 10.88 102 2 56

Explanation / Answer

> x=read.table("C:\Users\Admin\Desktop\pp.txt",header=TRUE)
> x
obs gpa iq gender concept
1 1 7.84 82 2 67
2 2 9.30 82 2 43
3 3 6.24 129 2 52
4 4 6.40 106 2 66
5 5 10.96 115 1 58
6 6 9.00 81 2 51
7 7 8.51 99 2 71
8 8 10.02 79 2 51
9 9 6.74 98 1 49
10 10 10.02 106 2 51
11 11 10.69 107 1 35
12 12 2.31 122 1 54
13 13 2.64 103 2 54
14 14 8.87 90 1 64
15 15 7.09 82 1 56
16 16 8.39 135 1 69
17 17 8.02 106 1 55
18 18 9.70 104 1 65
19 19 9.33 108 2 40
20 20 10.00 122 1 66
21 21 5.94 88 2 55
22 22 9.59 101 2 20
23 24 8.53 91 1 56
24 26 8.64 105 2 68
25 27 9.25 66 1 69
26 28 10.60 95 2 70
27 29 7.85 80 2 80
28 30 8.19 115 2 53
29 31 9.58 111 2 65
30 32 9.69 115 1 67
31 33 2.10 80 1 62
32 34 10.85 97 1 39
33 35 10.66 94 2 71
34 36 10.85 100 2 59
35 37 10.22 98 1 60
36 38 7.28 127 2 64
37 39 7.14 96 2 71
38 40 10.42 109 1 72
39 41 8.81 112 1 54
40 43 10.66 95 2 64
41 44 7.08 80 2 58
42 45 6.06 105 2 70
43 46 7.57 101 2 72
44 47 9.93 99 2 70
45 48 6.65 56 2 47
46 50 5.21 108 2 52
47 51 9.66 93 1 46
48 52 10.15 83 2 66
49 53 9.26 92 2 67
50 54 8.61 81 2 63
51 55 8.73 91 2 53
52 56 10.20 87 2 67
53 57 7.91 119 2 61
54 58 7.84 93 1 54
55 59 7.47 96 1 60
56 60 9.58 100 1 60
57 61 10.73 83 2 63
58 62 9.48 113 2 30
59 63 9.88 109 2 54
60 64 8.82 105 2 66
61 65 4.21 132 2 44
62 68 10.95 82 2 49
63 69 10.56 121 1 44
64 71 8.84 106 2 67
65 72 9.12 93 1 64
66 74 5.94 102 2 73
67 76 6.53 109 2 59
68 77 7.46 120 1 37
69 78 10.88 107 1 63
70 79 4.08 120 2 36
71 80 10.06 111 1 64
72 83 10.91 113 2 42
73 84 5.25 104 1 28
74 85 4.62 99 1 60
75 86 7.82 112 1 70
76 87 6.94 104 2 51
77 88 9.94 111 1 21
78 89 10.88 102 2 56
> IQ=x[,3]

a]

> Xbar= mean(IQ)
> Xbar
[1] 100.9359
> var=var(IQ)
> s1=sqrt(var)
> s1
[1] 14.85544

b]

> Median=median(IQ)
> Median
[1] 102

c]

> GPA=x[,2]
> head(GPA)
[1] 7.84 9.30 6.24 6.40 10.96 9.00
> Mean=mean(GPA)
> Mean
[1] 8.393974
> Median1=median(GPA)
> Median1
[1] 8.83

The data is a little skewed, and there are some outliers. Outliers can cause the mean to be affected much more than the median.

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