-->a=fscanfMat('data')
 a  =
 
    20.    35.    44.  
    37.    39.    37.  
    30.    43.    44.  
    27.    54.    49.  
    53.    42.    44.  
    58.    55.    37.  
    53.    46.    56.  
    46.    53.    59.  
    53.    49.    65.  
    43.    74.    53.  
    59.    60.    54.  
    52.    78.    74.  
    59.    70.    79.  
    62.    89.    74.  
    75.    65.    85.  
    59.    83.    84.  
    76.    78.    90.  
    91.    86.    71.  
    87.    91.    75.  
 
-->mean(a,'r')
 ans  =
 
    54.736842    62.631579    61.789474  
 
-->stdev(a,'r')
 ans  =
 
    18.958557    18.18183    17.018222  
 
-->size(a)
 ans  =
 
    19.    3.  
 
-->b=center(a,1)
 b  =
 
  - 34.736842  - 27.631579  - 17.789474  
  - 17.736842  - 23.631579  - 24.789474  
  - 24.736842  - 19.631579  - 17.789474  
  - 27.736842  - 8.6315789  - 12.789474  
  - 1.7368421  - 20.631579  - 17.789474  
    3.2631579  - 7.6315789  - 24.789474  
  - 1.7368421  - 16.631579  - 5.7894737  
  - 8.7368421  - 9.6315789  - 2.7894737  
  - 1.7368421  - 13.631579    3.2105263  
  - 11.736842    11.368421  - 8.7894737  
    4.2631579  - 2.6315789  - 7.7894737  
  - 2.7368421    15.368421    12.210526  
    4.2631579    7.3684211    17.210526  
    7.2631579    26.368421    12.210526  
    20.263158    2.3684211    23.210526  
    4.2631579    20.368421    22.210526  
    21.263158    15.368421    28.210526  
    36.263158    23.368421    9.2105263  
    32.263158    28.368421    13.210526  
 
-->c=b'*b // Note that I forgot to divide by 1/(N-1) [N=19 here]
 c  =
 
    6469.6842    4512.1579    3954.9474  
    4512.1579    5950.4211    4260.5263  
    3954.9474    4260.5263    5213.1579  
 
 
-->[p,d]=spec(c)
 d  =
 
    1286.7455    0.           0.        
    0.           1948.7978    0.        
    0.           0.           14397.72  
 p  =
 
  - 0.1355251    0.7858125    0.6034332  
    0.7365276  - 0.3274664    0.5918554  
  - 0.6626915  - 0.5246565    0.5343926  
 
-->a*p(:,3)
 ans  =
 
    56.296881  
    65.181919  
    67.066057  
    74.43813   
    80.353165  
    87.323703  
    89.133298  
    90.655432  
    95.718398  
    98.067741  
    99.971089  
    117.08831  
    119.24946  
    129.63305  
    129.15147  
    129.61554  
    140.12099  
    143.75387  
    146.43698  
 
-->b*p(:,3)
 ans  =
 
  - 46.821828  
  - 37.936791  
  - 36.052653  
  - 28.680579  
  - 22.765544  
  - 15.795006  
  - 13.985411  
  - 12.463277  
  - 7.4003108  
  - 5.0509684  
  - 3.1476207  
    13.969598  
    16.13075   
    26.51434   
    26.03276   
    26.496834  
    37.002277  
    40.635158  
    43.318273  
 
-->b*p(:,3)/sum(p(:,3))
 ans  =
 
  - 27.069628  
  - 21.932821  
  - 20.843524  
  - 16.581424  
  - 13.161699  
  - 9.1317435  
  - 8.0855421  
  - 7.205534   
  - 4.2784245  
  - 2.9201729  
  - 1.8197692  
    8.0763998  
    9.3258508  
    15.329032  
    15.050611  
    15.318911  
    21.39254   
    23.492859  
    25.044078  

// Note that this ranking puts student 14 slightly above students 15 and 16.
// But the race for 4th place is still too close to call.