Find the linear correlation coefficient between cumulative GPA and high school (HSP) percentile for the 200 UWEC undergraduate students in the Focus Sample SEX HSP GPA AGE CREDITS F 75 2.39 22 78 M 63 3.37 21 90 F 77 2.63 22 112 M 66 2.77 21 52 M 86 3.79 22 123 M 96 3.34 21 61 F 64 2.81 20 23 F 78 3.09 22 104 M 63 1.91 20 39 F 51 2.61 23 80 F 65 3.17 20 47 F 94 3.79 22 101 M 54 3.14 20 57 F 76 2.21 22 121 F 71 3.12 21 96 F 74 3.42 22 137 F 80 3.25 21 63 M 55 2.34 21 100 F 61 2.76 19 32 M 66 1.95 19 30 F 89 2.59 20 27 M 90 3.58 22 125 M 86 2.67 23 110 F 43 2.1 23 49 M 82 3.1 19 28 M 47 2.78 22 104 M 92 3.76 21 105 F 57 3.33 20 26 F 90 3.28 21 54 F 55 2.33 24 102 M 56 2.45 23 136 F 67 3.56 19 36 M 96 3.13 19 34 M 63 4 18 18 F 83 3.17 20 62 M 61 3.03 22 109 M 79 2.82 19 30 F 60 2.89 20 58 M 79 3.66 21 109 F 62 2.43 27 153 M 91 3.07 19 30 F 77 3.48 20 53 F 95 3.31 19 31 F 80 3.63 21 99 M 48 2.41 20 29 F 84 2.93 21 90 F 97 3.75 19 34 M 35 2.19 21 87 F 69 2.95 21 99 F 70 2.37 21 69 M 85 3.51 20 62 F 94 3.29 23 151 M 65 3.84 20 59 M 87 3.14 21 59 M 19 2.79 22 108 F 72 3.12 20 63 M 81 2.29 21 84 M 90 1.5 19 14 F 90 3.6 21 142 F 94 3.82 20 72 F 54 3.37 22 75 M 59 2.03 20 43 F 87 2.66 22 85 M 54 2.14 20 20 M 91 3.08 23 115 M 70 3.07 20 62 M 61 3.09 22 109 M 56 2.53 22 71 F 73 2.9 21 57 M 90 3.67 18 16 F 87 3.08 22 87 F 47 2.02 19 22 M 80 3.18 21 62 F 69 3 18 3 M 76 2.84 20 55 F 82 2.44 21 71 M 56 1.75 19 29 F 75 3.33 21 90 F 70 2.16 19 32 F 58 3.09 19 30 F 75 2.95 20 62 M 72 2.43 19 28 F 91 3.38 20 74 M 95 3.81 22 103 F 88 3.09 21 94 M 47 2.37 19 25 F 73 3.67 18 3 F 90 3.24 21 56 F 62 3.42 21 97 M 64 2.75 20 56 M 68 2.84 18 6 F 86 3.22 20 65 F 79 2.25 19 30 F 95 3.01 20 67 M 65 2.8 20 30 F 75 3.31 19 31 M 60 3.44 23 136 M 47 2.32 21 70 M 91 3.74 19 50 F 46 2.93 19 33 M 82 2.9 22 94 F 87 3.15 22 134 M 80 2.38 22 109 F 74 2.46 21 55 F 75 2.1 19 29 F 98 3.88 22 133 F 92 3.38 22 123 F 67 3.06 20 30 F 79 3.35 18 14 F 66 2.85 21 91 F 77 2.77 22 103 F 89 3.28 18 20 F 62 2.66 20 56 M 53 2.22 22 71 M 54 2.7 24 154 F 74 2.46 21 61 F 96 3.11 19 30 F 57 2.43 20 70 F 60 2.69 21 75 F 49 3.51 21 83 M 68 2.59 20 59 M 94 3.14 22 117 M 78 2.24 20 49 F 76 2.88 21 120 M 54 2.64 20 35 M 63 2.94 35 136 M 72 2.76 20 31 M 94 3.9 21 115 F 57 2.79 19 29 M 72 3.15 22 90 M 62 3.13 21 88 M 75 3.32 21 77 F 83 2.72 19 30 M 69 2.41 22 95 M 49 2.41 20 33 F 92 3.94 22 92 F 91 3.26 22 76 F 79 1.71 19 23 M 87 2.6 20 63 F 83 2.56 23 131 F 68 2.23 19 23 M 92 3.6 22 91 M 46 2.63 21 58 M 60 2.73 22 126 F 83 2.91 20 47 M 67 2.65 21 92 F 82 3.28 20 62 F 90 3.16 21 66 F 93 3.88 18 49 F 85 3.16 23 136 F 63 2.31 20 43 M 78 2.89 23 116 M 56 3.15 22 89 F 57 2.97 20 58 M 38 2.91 22 93 F 81 3.07 20 67 F 95 3.69 19 32 M 28 2.62 23 114 F 95 3.98 21 86 F 87 3.25 19 35 M 97 3.96 20 62 M 68 2.57 21 84 F 71 3.5 18 12 F 88 3.16 20 60 F 63 2.4 20 41 F 84 3.33 20 69 F 75 2.55 19 30 F 59 2.85 19 41 F 75 2.86 20 57 F 78 3.35 20 52 F 76 2.21 20 36 F 94 3.2 21 65 F 65 2.67 21 99 F 77 3.43 22 116 F 40 2.2 35 71 F 67 3.3 22 136 M 95 3.02 22 77 F 85 2.37 20 60 F 71 3.75 19 29 F 96 3.72 20 64 F 56 2.21 22 86 M 88 3.47 21 99 F 88 3.5 22 87 M 85 3.2 20 69 M 71 2.96 20 30 M 99 3.4 22 123 M 65 2.95 24 139 M 77 2.71 22 112 M 83 2.43 19 38 F 64 2.42 21 62 F 97 3.5 19 44 F 54 2.55 22 77 F 81 2.44 32 92 F 80 2.47 21 75 F 94 3.25 18 8 F 37 2.64 20 30 F 85 3.54 21 83 F 95 3.66 20 50 F 84 2.85 22 129 F 75 3.05 20 52
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
SEX | HSP | GPA | AGE | CREDITS |
F | 75 | 2.39 | 22 | 78 |
M | 63 | 3.37 | 21 | 90 |
F | 77 | 2.63 | 22 | 112 |
M | 66 | 2.77 | 21 | 52 |
M | 86 | 3.79 | 22 | 123 |
M | 96 | 3.34 | 21 | 61 |
F | 64 | 2.81 | 20 | 23 |
F | 78 | 3.09 | 22 | 104 |
M | 63 | 1.91 | 20 | 39 |
F | 51 | 2.61 | 23 | 80 |
F | 65 | 3.17 | 20 | 47 |
F | 94 | 3.79 | 22 | 101 |
M | 54 | 3.14 | 20 | 57 |
F | 76 | 2.21 | 22 | 121 |
F | 71 | 3.12 | 21 | 96 |
F | 74 | 3.42 | 22 | 137 |
F | 80 | 3.25 | 21 | 63 |
M | 55 | 2.34 | 21 | 100 |
F | 61 | 2.76 | 19 | 32 |
M | 66 | 1.95 | 19 | 30 |
F | 89 | 2.59 | 20 | 27 |
M | 90 | 3.58 | 22 | 125 |
M | 86 | 2.67 | 23 | 110 |
F | 43 | 2.1 | 23 | 49 |
M | 82 | 3.1 | 19 | 28 |
M | 47 | 2.78 | 22 | 104 |
M | 92 | 3.76 | 21 | 105 |
F | 57 | 3.33 | 20 | 26 |
F | 90 | 3.28 | 21 | 54 |
F | 55 | 2.33 | 24 | 102 |
M | 56 | 2.45 | 23 | 136 |
F | 67 | 3.56 | 19 | 36 |
M | 96 | 3.13 | 19 | 34 |
M | 63 | 4 | 18 | 18 |
F | 83 | 3.17 | 20 | 62 |
M | 61 | 3.03 | 22 | 109 |
M | 79 | 2.82 | 19 | 30 |
F | 60 | 2.89 | 20 | 58 |
M | 79 | 3.66 | 21 | 109 |
F | 62 | 2.43 | 27 | 153 |
M | 91 | 3.07 | 19 | 30 |
F | 77 | 3.48 | 20 | 53 |
F | 95 | 3.31 | 19 | 31 |
F | 80 | 3.63 | 21 | 99 |
M | 48 | 2.41 | 20 | 29 |
F | 84 | 2.93 | 21 | 90 |
F | 97 | 3.75 | 19 | 34 |
M | 35 | 2.19 | 21 | 87 |
F | 69 | 2.95 | 21 | 99 |
F | 70 | 2.37 | 21 | 69 |
M | 85 | 3.51 | 20 | 62 |
F | 94 | 3.29 | 23 | 151 |
M | 65 | 3.84 | 20 | 59 |
M | 87 | 3.14 | 21 | 59 |
M | 19 | 2.79 | 22 | 108 |
F | 72 | 3.12 | 20 | 63 |
M | 81 | 2.29 | 21 | 84 |
M | 90 | 1.5 | 19 | 14 |
F | 90 | 3.6 | 21 | 142 |
F | 94 | 3.82 | 20 | 72 |
F | 54 | 3.37 | 22 | 75 |
M | 59 | 2.03 | 20 | 43 |
F | 87 | 2.66 | 22 | 85 |
M | 54 | 2.14 | 20 | 20 |
M | 91 | 3.08 | 23 | 115 |
M | 70 | 3.07 | 20 | 62 |
M | 61 | 3.09 | 22 | 109 |
M | 56 | 2.53 | 22 | 71 |
F | 73 | 2.9 | 21 | 57 |
M | 90 | 3.67 | 18 | 16 |
F | 87 | 3.08 | 22 | 87 |
F | 47 | 2.02 | 19 | 22 |
M | 80 | 3.18 | 21 | 62 |
F | 69 | 3 | 18 | 3 |
M | 76 | 2.84 | 20 | 55 |
F | 82 | 2.44 | 21 | 71 |
M | 56 | 1.75 | 19 | 29 |
F | 75 | 3.33 | 21 | 90 |
F | 70 | 2.16 | 19 | 32 |
F | 58 | 3.09 | 19 | 30 |
F | 75 | 2.95 | 20 | 62 |
M | 72 | 2.43 | 19 | 28 |
F | 91 | 3.38 | 20 | 74 |
M | 95 | 3.81 | 22 | 103 |
F | 88 | 3.09 | 21 | 94 |
M | 47 | 2.37 | 19 | 25 |
F | 73 | 3.67 | 18 | 3 |
F | 90 | 3.24 | 21 | 56 |
F | 62 | 3.42 | 21 | 97 |
M | 64 | 2.75 | 20 | 56 |
M | 68 | 2.84 | 18 | 6 |
F | 86 | 3.22 | 20 | 65 |
F | 79 | 2.25 | 19 | 30 |
F | 95 | 3.01 | 20 | 67 |
M | 65 | 2.8 | 20 | 30 |
F | 75 | 3.31 | 19 | 31 |
M | 60 | 3.44 | 23 | 136 |
M | 47 | 2.32 | 21 | 70 |
M | 91 | 3.74 | 19 | 50 |
F | 46 | 2.93 | 19 | 33 |
M | 82 | 2.9 | 22 | 94 |
F | 87 | 3.15 | 22 | 134 |
M | 80 | 2.38 | 22 | 109 |
F | 74 | 2.46 | 21 | 55 |
F | 75 | 2.1 | 19 | 29 |
F | 98 | 3.88 | 22 | 133 |
F | 92 | 3.38 | 22 | 123 |
F | 67 | 3.06 | 20 | 30 |
F | 79 | 3.35 | 18 | 14 |
F | 66 | 2.85 | 21 | 91 |
F | 77 | 2.77 | 22 | 103 |
F | 89 | 3.28 | 18 | 20 |
F | 62 | 2.66 | 20 | 56 |
M | 53 | 2.22 | 22 | 71 |
M | 54 | 2.7 | 24 | 154 |
F | 74 | 2.46 | 21 | 61 |
F | 96 | 3.11 | 19 | 30 |
F | 57 | 2.43 | 20 | 70 |
F | 60 | 2.69 | 21 | 75 |
F | 49 | 3.51 | 21 | 83 |
M | 68 | 2.59 | 20 | 59 |
M | 94 | 3.14 | 22 | 117 |
M | 78 | 2.24 | 20 | 49 |
F | 76 | 2.88 | 21 | 120 |
M | 54 | 2.64 | 20 | 35 |
M | 63 | 2.94 | 35 | 136 |
M | 72 | 2.76 | 20 | 31 |
M | 94 | 3.9 | 21 | 115 |
F | 57 | 2.79 | 19 | 29 |
M | 72 | 3.15 | 22 | 90 |
M | 62 | 3.13 | 21 | 88 |
M | 75 | 3.32 | 21 | 77 |
F | 83 | 2.72 | 19 | 30 |
M | 69 | 2.41 | 22 | 95 |
M | 49 | 2.41 | 20 | 33 |
F | 92 | 3.94 | 22 | 92 |
F | 91 | 3.26 | 22 | 76 |
F | 79 | 1.71 | 19 | 23 |
M | 87 | 2.6 | 20 | 63 |
F | 83 | 2.56 | 23 | 131 |
F | 68 | 2.23 | 19 | 23 |
M | 92 | 3.6 | 22 | 91 |
M | 46 | 2.63 | 21 | 58 |
M | 60 | 2.73 | 22 | 126 |
F | 83 | 2.91 | 20 | 47 |
M | 67 | 2.65 | 21 | 92 |
F | 82 | 3.28 | 20 | 62 |
F | 90 | 3.16 | 21 | 66 |
F | 93 | 3.88 | 18 | 49 |
F | 85 | 3.16 | 23 | 136 |
F | 63 | 2.31 | 20 | 43 |
M | 78 | 2.89 | 23 | 116 |
M | 56 | 3.15 | 22 | 89 |
F | 57 | 2.97 | 20 | 58 |
M | 38 | 2.91 | 22 | 93 |
F | 81 | 3.07 | 20 | 67 |
F | 95 | 3.69 | 19 | 32 |
M | 28 | 2.62 | 23 | 114 |
F | 95 | 3.98 | 21 | 86 |
F | 87 | 3.25 | 19 | 35 |
M | 97 | 3.96 | 20 | 62 |
M | 68 | 2.57 | 21 | 84 |
F | 71 | 3.5 | 18 | 12 |
F | 88 | 3.16 | 20 | 60 |
F | 63 | 2.4 | 20 | 41 |
F | 84 | 3.33 | 20 | 69 |
F | 75 | 2.55 | 19 | 30 |
F | 59 | 2.85 | 19 | 41 |
F | 75 | 2.86 | 20 | 57 |
F | 78 | 3.35 | 20 | 52 |
F | 76 | 2.21 | 20 | 36 |
F | 94 | 3.2 | 21 | 65 |
F | 65 | 2.67 | 21 | 99 |
F | 77 | 3.43 | 22 | 116 |
F | 40 | 2.2 | 35 | 71 |
F | 67 | 3.3 | 22 | 136 |
M | 95 | 3.02 | 22 | 77 |
F | 85 | 2.37 | 20 | 60 |
F | 71 | 3.75 | 19 | 29 |
F | 96 | 3.72 | 20 | 64 |
F | 56 | 2.21 | 22 | 86 |
M | 88 | 3.47 | 21 | 99 |
F | 88 | 3.5 | 22 | 87 |
M | 85 | 3.2 | 20 | 69 |
M | 71 | 2.96 | 20 | 30 |
M | 99 | 3.4 | 22 | 123 |
M | 65 | 2.95 | 24 | 139 |
M | 77 | 2.71 | 22 | 112 |
M | 83 | 2.43 | 19 | 38 |
F | 64 | 2.42 | 21 | 62 |
F | 97 | 3.5 | 19 | 44 |
F | 54 | 2.55 | 22 | 77 |
F | 81 | 2.44 | 32 | 92 |
F | 80 | 2.47 | 21 | 75 |
F | 94 | 3.25 | 18 | 8 |
F | 37 | 2.64 | 20 | 30 |
F | 85 | 3.54 | 21 | 83 |
F | 95 | 3.66 | 20 | 50 |
F | 84 | 2.85 | 22 | 129 |
F | 75 | 3.05 | 20 | 52 |
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