Grade Distribution Processing for CG1

Proposer:
  - Changkun Ou <changkun.ou at ifi.lmu.de>

Approvers:
  - Andreas Butz <butz at ifi.lmu.de>
  - David Englmeier <david.englmeier at ifi.lmu.de>

======================================================================
Approach: Gamma correction

Step 1. We want grade > lo pass the exam and apply gamma correction

  (grade_low/grade_max) = (lo/grade_max)^gamma

Thus, compute gamma value using this formula:

   gamma = (log(grade_low/grade_max))/(log(lo/grade_max))

Step 2. re-corrected grades using the computed gamma value:

   grade = grade_max*(grade/grade_max)^gamma

Step 3. map the grade to credits using this table

       5.0 4.0 3.7 3.3 3.0 2.7 2.3 2.0 1.7 1.3 1.0
Points 0   100 110 120 130 140 150 160 170 180 190

Step 4. reset the grade to credits table based on the final grades.
Based on the computation, we have a new table for the grade computation:

    5.0:   0 <= x < 70
    4.0:  70 <= x < 81
    3.7:  81 <= x < 91
    3.0: 103 <= x < 114
    2.7: 114 <= x < 125
    2.3: 125 <= x < 140
    2.0: 140 <= x < 160
    1.7: 160 <= x < 170
    1.3: 170 <= x < 180
    1.0: 180 <= x <=220
======================================================================

valid submissions:

118

global points distribution:

9, 27, 36, 47, 48, 56, 57, 57, 60, 61, 69, 69, 74, 74, 76, 78,
80, 81, 82, 82, 82, 83, 83, 84, 84, 84, 84, 87, 88, 89, 90, 91,
92, 92, 93, 94, 95, 95, 97, 97, 100, 100, 100, 100, 101, 101,
101, 101, 101, 101, 101, 101, 102, 102, 103, 103, 104, 104, 104,
104, 105, 105, 105, 105, 105, 107, 107, 107, 107, 108, 108, 108,
108, 108, 109, 110, 110, 111, 111, 111, 111, 112, 113, 113, 113,
114, 115, 116, 116, 117, 117, 118, 118, 119, 119, 119, 119, 119,
119, 121, 123, 123, 127, 128, 131, 131, 132, 133, 134, 142, 143,
150, 161, 173, 176, 187, 192, 203

grade_max = 220
grade_low = 100
lo        = 70

==>

gamma     = 0.69

==>

original: 9    after: 24   grade: 5.0  scaling: +166.67%
original: 27   after: 52   grade: 5.0  scaling: +92.59%
original: 36   after: 63   grade: 5.0  scaling: +75.0%
original: 47   after: 76   grade: 5.0  scaling: +61.7%
original: 48   after: 77   grade: 5.0  scaling: +60.42%
original: 56   after: 86   grade: 5.0  scaling: +53.57%
original: 57   after: 87   grade: 5.0  scaling: +52.63%
original: 57   after: 87   grade: 5.0  scaling: +52.63%
original: 60   after: 90   grade: 5.0  scaling: +50.0%
original: 61   after: 91   grade: 5.0  scaling: +49.18%
original: 69   after: 99   grade: 5.0  scaling: +43.48%
original: 69   after: 99   grade: 5.0  scaling: +43.48%
original: 74   after: 104  grade: 4.0  scaling: +40.54%
original: 74   after: 104  grade: 4.0  scaling: +40.54%
original: 76   after: 106  grade: 4.0  scaling: +39.47%
original: 78   after: 108  grade: 4.0  scaling: +38.46%
original: 80   after: 109  grade: 4.0  scaling: +36.25%
original: 81   after: 110  grade: 3.7  scaling: +35.8%
original: 82   after: 111  grade: 3.7  scaling: +35.37%
original: 82   after: 111  grade: 3.7  scaling: +35.37%
original: 82   after: 111  grade: 3.7  scaling: +35.37%
original: 83   after: 112  grade: 3.7  scaling: +34.94%
original: 83   after: 112  grade: 3.7  scaling: +34.94%
original: 84   after: 113  grade: 3.7  scaling: +34.52%
original: 84   after: 113  grade: 3.7  scaling: +34.52%
original: 84   after: 113  grade: 3.7  scaling: +34.52%
original: 84   after: 113  grade: 3.7  scaling: +34.52%
original: 87   after: 116  grade: 3.7  scaling: +33.33%
original: 88   after: 117  grade: 3.7  scaling: +32.95%
original: 89   after: 118  grade: 3.7  scaling: +32.58%
original: 90   after: 119  grade: 3.7  scaling: +32.22%
original: 91   after: 120  grade: 3.3  scaling: +31.87%
original: 92   after: 121  grade: 3.3  scaling: +31.52%
original: 92   after: 121  grade: 3.3  scaling: +31.52%
original: 93   after: 121  grade: 3.3  scaling: +30.11%
original: 94   after: 122  grade: 3.3  scaling: +29.79%
original: 95   after: 123  grade: 3.3  scaling: +29.47%
original: 95   after: 123  grade: 3.3  scaling: +29.47%
original: 97   after: 125  grade: 3.3  scaling: +28.87%
original: 97   after: 125  grade: 3.3  scaling: +28.87%
original: 100  after: 128  grade: 3.3  scaling: +28.0%
original: 100  after: 128  grade: 3.3  scaling: +28.0%
original: 100  after: 128  grade: 3.3  scaling: +28.0%
original: 100  after: 128  grade: 3.3  scaling: +28.0%
original: 101  after: 129  grade: 3.3  scaling: +27.72%
original: 101  after: 129  grade: 3.3  scaling: +27.72%
original: 101  after: 129  grade: 3.3  scaling: +27.72%
original: 101  after: 129  grade: 3.3  scaling: +27.72%
original: 101  after: 129  grade: 3.3  scaling: +27.72%
original: 101  after: 129  grade: 3.3  scaling: +27.72%
original: 101  after: 129  grade: 3.3  scaling: +27.72%
original: 101  after: 129  grade: 3.3  scaling: +27.72%
original: 102  after: 129  grade: 3.3  scaling: +26.47%
original: 102  after: 129  grade: 3.3  scaling: +26.47%
original: 103  after: 130  grade: 3.0  scaling: +26.21%
original: 103  after: 130  grade: 3.0  scaling: +26.21%
original: 104  after: 131  grade: 3.0  scaling: +25.96%
original: 104  after: 131  grade: 3.0  scaling: +25.96%
original: 104  after: 131  grade: 3.0  scaling: +25.96%
original: 104  after: 131  grade: 3.0  scaling: +25.96%
original: 105  after: 132  grade: 3.0  scaling: +25.71%
original: 105  after: 132  grade: 3.0  scaling: +25.71%
original: 105  after: 132  grade: 3.0  scaling: +25.71%
original: 105  after: 132  grade: 3.0  scaling: +25.71%
original: 105  after: 132  grade: 3.0  scaling: +25.71%
original: 107  after: 134  grade: 3.0  scaling: +25.23%
original: 107  after: 134  grade: 3.0  scaling: +25.23%
original: 107  after: 134  grade: 3.0  scaling: +25.23%
original: 107  after: 134  grade: 3.0  scaling: +25.23%
original: 108  after: 135  grade: 3.0  scaling: +25.0%
original: 108  after: 135  grade: 3.0  scaling: +25.0%
original: 108  after: 135  grade: 3.0  scaling: +25.0%
original: 108  after: 135  grade: 3.0  scaling: +25.0%
original: 108  after: 135  grade: 3.0  scaling: +25.0%
original: 109  after: 136  grade: 3.0  scaling: +24.77%
original: 110  after: 136  grade: 3.0  scaling: +23.64%
original: 110  after: 136  grade: 3.0  scaling: +23.64%
original: 111  after: 137  grade: 3.0  scaling: +23.42%
original: 111  after: 137  grade: 3.0  scaling: +23.42%
original: 111  after: 137  grade: 3.0  scaling: +23.42%
original: 111  after: 137  grade: 3.0  scaling: +23.42%
original: 112  after: 138  grade: 3.0  scaling: +23.21%
original: 113  after: 139  grade: 3.0  scaling: +23.01%
original: 113  after: 139  grade: 3.0  scaling: +23.01%
original: 113  after: 139  grade: 3.0  scaling: +23.01%
original: 114  after: 140  grade: 2.7  scaling: +22.81%
original: 115  after: 141  grade: 2.7  scaling: +22.61%
original: 116  after: 141  grade: 2.7  scaling: +21.55%
original: 116  after: 141  grade: 2.7  scaling: +21.55%
original: 117  after: 142  grade: 2.7  scaling: +21.37%
original: 117  after: 142  grade: 2.7  scaling: +21.37%
original: 118  after: 143  grade: 2.7  scaling: +21.19%
original: 118  after: 143  grade: 2.7  scaling: +21.19%
original: 119  after: 144  grade: 2.7  scaling: +21.01%
original: 119  after: 144  grade: 2.7  scaling: +21.01%
original: 119  after: 144  grade: 2.7  scaling: +21.01%
original: 119  after: 144  grade: 2.7  scaling: +21.01%
original: 119  after: 144  grade: 2.7  scaling: +21.01%
original: 119  after: 144  grade: 2.7  scaling: +21.01%
original: 121  after: 146  grade: 2.7  scaling: +20.66%
original: 123  after: 147  grade: 2.7  scaling: +19.51%
original: 123  after: 147  grade: 2.7  scaling: +19.51%
original: 127  after: 151  grade: 2.3  scaling: +18.9%
original: 128  after: 151  grade: 2.3  scaling: +17.97%
original: 131  after: 154  grade: 2.3  scaling: +17.56%
original: 131  after: 154  grade: 2.3  scaling: +17.56%
original: 132  after: 155  grade: 2.3  scaling: +17.42%
original: 133  after: 155  grade: 2.3  scaling: +16.54%
original: 134  after: 156  grade: 2.3  scaling: +16.42%
original: 142  after: 163  grade: 2.0  scaling: +14.79%
original: 143  after: 163  grade: 2.0  scaling: +13.99%
original: 150  after: 169  grade: 2.0  scaling: +12.67%
original: 161  after: 177  grade: 1.7  scaling: +9.94%
original: 173  after: 186  grade: 1.3  scaling: +7.51%
original: 176  after: 189  grade: 1.3  scaling: +7.39%
original: 187  after: 197  grade: 1.0  scaling: +5.35%
original: 192  after: 200  grade: 1.0  scaling: +4.17%
original: 203  after: 208  grade: 1.0  scaling: +2.46%